The Bellini is a drink almost everyone has had and almost nobody has had properly. The version poured at most hotel brunches — peach schnapps, a splash of syrup, a bottle of whatever fizz was open, sometimes Champagne — has about as much to do with the original as a jarred sauce has to do with a Sunday ragù. The real thing is two ingredients, one of which you can only buy for a couple of months a year, and it was invented by a man who was trying to bottle the colour of a painting.

Here it is, stripped down: cold white peach purée, cold Prosecco, poured together in a chilled glass. No sugar if the peaches are ripe. No liqueur. No Champagne. That's the whole drink, and the fact that it's so simple is exactly why it goes wrong so often.

The painting

The Bellini was born at Harry's Bar in Venice — the small, plain, almost aggressively unshowy room near Piazza San Marco that Giuseppe Cipriani opened in 1931 and that went on to feed and water half the 20th century, Hemingway included. Cipriani mixed white peach purée with Prosecco sometime in the 1930s or 40s (the usual date is 1948, though Cipriani himself was vague about it), and he had it before he had a name for it.

The name came from a painting. The soft rose colour of the drink reminded Cipriani of the pink glow on a saint's robe in a work by Giovanni Bellini, the 15th-century Venetian master. So the cocktail became the Bellini — and it started a whole family of Harry's Bar drinks named after Venetian painters, which we'll get to.

Why the peach matters more than anything

The single non-negotiable ingredient is the white peach. Not yellow peaches, which are more acidic and more assertive. White peaches are floral, delicate, low-acid, and faintly perfumed, and their pale flesh gives the drink its characteristic soft pink rather than a brash orange. Cipriani used white peaches from the Veneto, in season, and when they weren't in season he didn't fake it — Harry's Bar served other drinks the rest of the year.

That's the part the brunch industry quietly dropped. A proper Bellini is a seasonal drink, tied to the roughly two months — July and August in the northern hemisphere — when white peaches are ripe and cheap and dripping. You can freeze the purée to stretch the season, and plenty of Venetian bars do. But a Bellini made with tinned peaches or peach nectar in February is a different, sadder drink wearing the same name.

The second rule: it must be Prosecco, not Champagne. Cipriani built the drink around Prosecco's softer, fruitier, less austere bubble. Use Champagne and you've technically made something else — the drink's balance tips from gentle to sharp. If you want the Champagne version, fine, but call it what the French call it and accept it isn't a Bellini.

The recipe

You'll need (makes about 6)

Method

1. Peel the peaches (drop them in boiling water for 20 seconds and the skins slip off), remove the stones, and blend the flesh to a smooth purée with the lemon juice. For a silkier drink, push it through a fine sieve. Chill it thoroughly — the purée must be cold going in.

2. Spoon a generous measure of cold purée into the bottom of a chilled glass — roughly one part purée.

3. Add the Prosecco slowly, in two or three pours, stirring gently between each — roughly two to three parts Prosecco to one part purée. Pour too fast and it foams over the top; the purée makes the fizz lively.

4. Give it one final gentle stir to bring the peach up from the bottom. No garnish. Harry's Bar serves it in a small tumbler rather than a flute — a detail worth copying. Drink it cold and soon.

The painter cocktails

Once the Bellini existed, Harry's Bar kept going with the same idea — seasonal fruit purée plus Prosecco, each named after a great Italian painter or composer. It's a genuinely useful template, because it tells you exactly what to make when white peaches are out of season.

(The Mimosa — orange juice and sparkling wine — is the French cousin of this idea, not a Harry's Bar drink, and it's a coarser thing. Fresh-squeezed orange is a world away from the peach's perfume.)

The colour

Cipriani named the drink for a colour — the rose of a saint's robe in a Bellini painting — and that colour only shows up if the peach is real. Make it with syrup or nectar and you can get close on flavour, but the pink goes wrong: flat, orange, a little sad. The whole thing was always about getting that one shade right, which is why he served it only for the two months a year the peaches allowed. Drink one then, in a cold tumbler, and you'll see the colour he meant. The brunch version, for all its convenience, never quite gets there.