We used fresh apricots in this creamy tart, but fresh peaches or nectarines would be just as suitable. The smooth, sweet filling, enriched with ricotta cheese and just a bit of heavy cream, contrasts appealingly with the tart stone fruit.
Crust: In a medium-sized mixing bowl, cream the butter until light and fluffy. Add the sugar, salt and vanilla. Beat in the egg and half the flour, then add the remaining flour and mix until evenly blended. Gather the dough into a ball, flatten it into a thick disk, wrap it well, and refrigerate for 1 hour. Heavily flour your work surface and the dough. Roll the dough to fit a 10-inch tart pan or a 9-inch deep-dish pie pan. Place the dough in the pan, and prick it all over with the tines of a fork. (The crust will be blind-baked -- baked without any filling -- but it doesn't need to be weighed down with beans or rice or pie weights, as long as you prick it thoroughly with a fork.).
Bake the crust in a preheated 425°F oven for 10 minutes. Turn the oven down to 350°F, and bake it until it's golden brown, about another 8 to 10 minutes. Remove the crust from the oven and cool it while making the filling.
Filling: In a medium-sized bowl, mix together the ricotta cheese, cream, eggs, egg yolk, sugar, vanilla, Fiori di Sicilia or orange oil, and flour. Set aside.
Peel and slice the apricots. To quickly peel apricots, fill a large pan with hot water. Bring it to a boil, and place the apricots in the pan. Bring back to a boil, and simmer for 2 to 3 minutes. Remove the apricots from the hot water and plunge them into a bowl of ice water. The skins should slip off easily.
Assembly and Baking: Stone and slice the apricots. Pour the ricotta mixture into the tart shell. Place about 10 slices of apricot over the filling; they'll sink partially -- it's OK. Bake the tart in a preheated 350°F oven for about 45 minutes, until the filling looks mostly set.
Sauce: Place the remaining sliced apricots into a medium-sized saucepan. Add the brown sugar, water, and brandy, if you're using it. Bring the mixture to a gentle boil, reduce the heat, and simmer until the apricots are cooked through and the sauce starts to thicken. Remove the sauce from the heat, and transfer it to a serving dish. It can remain at room temperature while the tart cools.
Let the ricotta tart cool for several hours before cutting it into wedges. Spoon the sauce over each piece before serving, or serve it on the side. Refrigerate any leftover tart.