In the bowl of a stand mixer fitted with a paddle attachment, beat the cream cheese and sugar on medium speed until smooth and fluffy, about 2 to 3 minutes. Add 1/4 cup flour, cream, and vanilla. Beat on medium until smooth, about 1 minute. Add the eggs, one at a time, beating well after each addition and stopping to scrape down the bowl frequently.
Remove 1 cup of batter, and place in a small bowl. Stir the melted chocolate into the batter.
In another small bowl, whisk together the caramel and the remaining 2 teaspoons of flour. Stir in the chopped pecans. Spread the caramel mixture in an even layer over the cooled crust. Spread the chocolate batter into an even layer over the caramel mixture. Carefully spoon the plain batter over the chocolate filling, and smooth the top. Place on a baking sheet.
Bring 8 cups of water to a boil. Place a large roasting pan or casserole dish on the bottom rack of the oven and carefully fill halfway with the boiling water. Place the cheesecake on the middle rack.
Bake for 75 to 90 minutes or until the edges are pulling away slightly from the sides of the pan and the center wobbles when gently shaken. Cover the cheesecake loosely with foil after 60 minutes if the top appears to be browning too quickly. Remove from the oven and let cool on a wire rack, for 1 hour. Refrigerate, uncovered, for at least 4 hours and up to 2 days.