Preheat the oven to 350°F and position a rack in the center. Lightly grease a 10-inch springform pan with nonstick cooking spray or butter. Sprinkle a couple of tablespoons of granulated sugar into the pan and swirl it around to coat the bottom and sides evenly, tapping out the excess sugar. Line the outside of the pan with a sheet of aluminum foil to guard against any leaks. The cheesecake will be baked in a water bath, so have ready a deep roasting pan that is large enough to accommodate the springform pan with an inch of space on all sides.
In an electric mixer fitted with the paddle attachment, beat together the yogurt, mascarpone, remaining ¾ cup granulated sugar, and confectioners sugar on medium speed until very smooth and creamy, about 1 minute, stopping once to scrape down the sides of the bowl. Beat in the eggs and egg yolks one at a time, followed by the salt and vanilla extract, scraping down the sides of the bowl after each addition.
Pour the batter into the prepared pan, smoothing the top with a spatula. Place the springform pan in the roasting pan and carefully fill the roasting pan with enough hot water to come halfway up the sides of the springform pan. Cover both pans with a single piece of aluminum foil, tenting the foil so it does not touch the top of the springform pan and being sure to cover the roasting pan completely. Very carefully transfer the roasting pan to the oven.
Bake the cheesecake for 20 minutes, then carefully rotate the pan 180 degrees to ensure that the cake bakes evenly. Bake for another 2 minutes, then remove the foil tent. The cake should be puffed but not cracked, jiggly but not liquid in the center. If necessary, continue baking the cake without the foil until it is set.
Remove the roasting pan from the oven and allow the cake to cool in the water bath until the water is lukewarm. Carefully remove the springform pan from the roasting pan and continue cooling the cake on a rack until it is cool to the touch. Remove the foil from the outside of the pan and chill the cake in the refrigerator 8 hours or overnight.
Before serving, remove the sides of the springform pan; you may have to run a knife around the edges. Transfer the cheesecake to a serving plate or cake stand and sprinkle the top with some chopped pine nut brittle. To serve, cut the cheesecake into wedges with a long, thin-bladed knife. Any leftover cake may be wrapped in plastic and stored in the refrigerator for up to 3 days.