For the topping: Put all of the ingredients except the extract in the bowl of a stand mixer fitted with the paddle attachment, or a large bowl you can use with a hand mixer, and mix on low speed until you have very moist clumps and curds. Beat in the vanilla. Turn the dough out onto a work surface, knead it into a cohesive ball and shape it into a disk. Roll out the dough until it’s between ⅛ inch thick. Slide the dough onto a baking sheet and put in the freezer until needed.

For the puffs: Preheat the oven to 425 degrees F. Draw 12 circles on a piece of parchment paper, flip it over and use it to line a baking sheet. Put the milk, water, butter, sugar, and salt in a medium saucepan and bring to a boil. Add the flour all at once and beat until you’ve got a dough that pulls away from the pan. Turn the dough out into a bowl and add the eggs one at a time, beating for a minute after each. Scrape the dough into a pastry bag and pipe out a dozen puffs.

Remove the topping from the freezer, cut out a dozen rounds, and balance a circle of topping on each puff. Bake for 5 minutes, then turn the oven down to 350 degrees F and bake for another 35 minutes. Let the puffs dry in the oven for 15 to 20 minutes.

For the cream filling: Beat the cream on medium speed until it holds soft peaks. Beat in the sugar and vanilla until the cream holds its shape.

To fill the puffs: Cut each puff in half and fill with cream. Serve immediately or refrigerate briefly.