Preheat oven to 350 degrees F (175 degrees C). Line a 9-inch springform pan with parchment paper.
Combine almond flour, brown sugar, and almonds in a bowl. Add melted butter; stir with a fork until the mixture resembles wet sand. Spread on the bottom of the parchment-lined pan.
Combine apricots and water in a saucepan; bring to a boil and simmer until very soft, about 10 minutes. Drain; mash apricots into a pulp. Add amaretto; mix well. Sweeten with 1 teaspoon white sugar.
Beat cream cheese, 3/4 cup white sugar, 1/2 cup sour cream, cornstarch, and 1 1/2 teaspoons vanilla extract in a bowl using an electric mixer on low speed. Add eggs one at a time; mix well. Fold in 2 tablespoons of apricot pulp; reserve remainder for topping. Pour cheesecake batter into the pan, covering the crust.
Bake in the preheated oven until edges are puffed and surface of cheesecake is firm except for a small spot in the center that will jiggle when the pan is gently shaken, about 45 minutes.
Beat 1 1/2 cups sour cream, 3 tablespoons white sugar, and 1 teaspoon vanilla extract together until combined. Remove cheesecake from the hot oven; spoon topping over the surface and return cake to the oven for 8 minutes more.
Cool to room temperature, about 1 hour. Refrigerate for 6 to 8 hours. Top with remaining apricot pulp.