Bring about 2 inches of water to a simmer in a large saucepan. In a mixer fitted with a whisk attachment (or using a hand mixer), whip the eggs and sugar together until very light yellow and fluffy. Mix in the lemon juice and lemon zest. Rest the mixing bowl in the saucepan, with the bowl's base resting above--not in--the simmering water (pour out some water if necessary). Cook, whisking occasionally, until the mixture is thickened and custardy, about 10 minutes.
Meanwhile, half-fill a large bowl with ice and cover with cold water. Remove the bowl with the custard in it from the hot water and whisk in the butter until melted. Rest the bottom of the bowl in the ice bath and let cool, folding the mixture occasionally to cool and thicken it. In a mixer fitted with a whisk attachment (or using a hand mixer), whip the cream until stiff. Fold into the cooled lemon custard. Cover and refrigerate until ready to serve. (The recipe can be made up to this point and kept refrigerated up to 3 days in advance.)
Heat the oven to 350 degrees F. Flour a work surface and lay out the puff pastry. Roll the sheets lightly with a rolling pin until smooth and flat. Use a 2-inch fluted cookie cutter to cut out rounds from the puff pastry. Cut out the centers by pushing halfway down with a 1-inch plain round small cookie cutter. Do not pull out the centers yet; you'll do that after they are baked. Arrange on a parchment-lined cookie sheet and bake until golden brown, 15 to 20 minutes. After 10 minutes, rotate the pan to ensure even cooking. When baked, immediately remove to a wire rack and let cool to room temperature.
Cut around the centers with a paring knife to loosen, but don't cut all the way through to the bottom. You want to leave a thin layer of pastry to hold the filling. Pull out the centers to make a hollow in the center of each pastry round. Before serving, spoon or pipe a generous dollop of custard into each pastry round. Sprinkle the custard with chopped pistachios. Serve within 6 hours.