Preheat the oven to 400 degrees F. Line a sheet pan with parchment paper.
Place the cream cheese and sugar in the bowl of an electric mixer fitted with a paddle attachment and cream them together on low speed until smooth. With the mixer still on low, add the egg yolks, ricotta, vanilla, salt, and lemon zest and mix until just combined. Don't whip!
Unfold 1 sheet of puff pastry onto a lightly floured board and roll it slightly with a floured rolling pin until it's a 10 by 10-inch square. Cut the sheet into quarters with a sharp knife. Place a heaping tablespoon of cheese filling into the middle of each of the 4 squares. Brush the border of each pastry with egg wash and fold 2 opposite corners to the center, brushing and overlapping the corners of each pastry so they firmly stick together. Brush the top of the pastries with egg wash. Place the pastries on the prepared sheet pan. Repeat with the second sheet of puff pastry and refrigerate the filled Danish for 15 minutes.
Bake the pastries for about 20 minutes, rotating the pan once during baking, until puffed and brown. Serve warm.