2 ripe peaches (see headnote)
2 ounces peach liqueur (we like Mathilde)
1 tablespoon fresh lemon juice
Chilled sparkling white wine (again, tradition prescribes Prosecco, but a decent not-too-dry Champagne or Champagne-style bubbly will suit)
Make the puree
Peel and seed the peaches, then cut them into small chunks.
Drop the peaches in a blender and add the liqueur, two tablespoons of water and the lemon juice.
Blend on high speed to make a puree; if necessary, stop and scrape down the sides of the blender jar. You may need to add more water to make the blender perform properly.
Pour the puree into a measuring cup and, if you don’t have a cup of puree, add additional water to make a cup.
(If you have a wimpy blender, you might need to strain the puree to remove small pieces of peach. In that case, don’t add any additional water, and just deal with the fact that your yield will be lower.)
Make the cocktail
Pour one ounce (two tablespoons) of puree into a 5- to 6-ounce champagne flute. Top with about 2 ounces of sparkling wine and stir to combine. Fill the glass with more sparkling wine, stir gently one more time, and serve.