In the bowl of a food processor, pulse flour, 2 tablespoons of sugar, 3/4 cup of pine nuts, and salt until finely ground. Add the butter. Pulse dough just until it comes together.
Place the dough into an 11-inch diameter tart pan with a removable bottom and press down to cover the bottom and sides of the pan. Refrigerate until the dough is firm, about 30 minutes.
Line the tart shell with aluminum foil and fill with pie weights or dried beans. Bake the tart shell in the lower third of the oven until just set, about 25 minutes. Carefully remove the foil and pie weights. Bake until the tart shell is lightly golden, about 10 minutes. Cool completely.
Combine the remaining 2 tablespoons of sugar with the water in a small saucepan over low heat. You don't want to boil the water, you just want to heat it so that the sugar can dissolve thoroughly. Stir until the sugar dissolves and remove from heat.
In the bowl of a food processor, pulse the ricotta cheese and cream cheese until smooth. Add the eggs and egg yolks, 1 at a time, and process until smooth. With the machine running, add the sugar syrup in a thin steady stream and process until smooth.
Pour the custard into the tart shell and bake until the filling is almost set, about 20 to 25 minutes. Scatter the remaining 3/4 cup of toasted pine nuts atop the filling. Bake until the custard is set, about 10 minutes longer. Let the tart cool completely before serving.
The tart can be wrapped in plastic and refrigerated for up to 3 days. Return the tart to room temperature before serving.