Preheat the oven to 350°. In a food processor, pulse the amaretti with the graham crackers and salt until finely ground. Transfer the crumbs to a small bowl and stir in the butter. Press the crumbs evenly over the bottom and halfway up the side of an 8-inch springform pan. Bake for about 10 minutes, until the crust is set. Cool on a rack.

In a microwave-safe dish, sprinkle the gelatin over 2 tablespoons of cold water; let stand until the gelatin is softened, about 10 minutes. Meanwhile, in a small bowl, beat the heavy cream until soft peaks form; refrigerate.

In a bowl, beat the cream cheese, ricotta, sugar and salt with an electric mixer at high speed until light and fluffy, about 5 minutes. Beat in the mascarpone and lemon juice.

Microwave the gelatin until melted, 5 seconds; scrape into the cream cheese mixture and beat until incorporated. Fold in the whipped cream. Pour the mixture into the cooled crust and smooth the surface. Refrigerate the cake until firm and set, 3 hours.

In a medium saucepan, combine the honey with 3 cups of water and the rosemary. Bring to a boil and cook over moderately high heat, stirring occasionally, until the honey is dissolved. Add the apricots and simmer until tender, 10 minutes. With a slotted spoon, transfer the apricots to a bowl. Boil the rosemary syrup until thickened, 20 to 25 minutes. Strain the syrup over the apricots and let cool.

Unmold the cheesecake and serve with the honeyed apricots.