Special equipment: a 9-inch springform pan; four 8-ouce ramekins
Preheat the oven to 350 degrees F.
Using a hand mixer, beat the cream cheese and 3/4 cup sugar in a large bowl until light and fluffy. Add 1 egg and mix until just combined. Pour the batter into a 9-inch springform pan and bake 40 minutes. Cool at room temperature for 10 minutes, and then refrigerate or freeze until firm, about 30 minutes.
Melt the butter in a large skillet over medium heat. Add the apples, cinnamon and remaining 1/2 cup sugar. Cook, stirring occasionally, until the apples are tender; cool.
Heat a griddle or large skillet over medium heat. Beat the remaining egg in a small bowl. Warm the tortillas on the griddle just until pliable, and then press them into four 8-ounce ramekins to make tortilla bowls. Put 4 caramel pieces, 1 heaping tablespoon of the apples and about 3 tablespoons of cheesecake into each tortilla bowl. (You will have some leftover cheesecake, which can be wrapped tightly and frozen for up to 2 weeks.)
Brush the edges of the tortillas with the beaten egg and close, pressing to seal. Refrigerate the cheesecake bombs to firm up again, about 3 hours.
Heat the vegetable oil in a deep-fryer or large pot to 365 degrees F.
Gently put the cheesecake bombs in the oil and fry until golden brown, about 2 minutes. Using tongs, remove the golden-brown bombs from the oil. Carefully blot away any excess oil with a paper towel. Put each bomb on a serving plate, drizzle with caramel sauce, and serve hot.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.
Recipe courtesy of Chef Todd Alexander, Chef Toddzilla's Mobile Cuisine, Roswell, NM