Preheat oven to 325°F. Place a large roasting pan on the lower third rack of the oven. Bring a kettle of water to a boil on the stove.
Prepare a 9-inch springform pan: spray the bottom and sides with nonstick spray, line the bottom with a round of parchment paper, then wrap a double layer of foil around the bottom and up the sides of the pan, sealing it so water from the water bath cannot seep into the pan.
In a large bowl, use an electric mixer to beat the Two 8-ounce packages cream cheese (room temperature) until smooth and creamy.
Add 2/3 cup granulated white sugar and a pinch of salt to the cream cheese and blend for about 2 minutes, scraping down the sides of the bowl as needed.
Add the 2 large eggs one at a time, mixing briefly after each egg until incorporated.
Add 1/3 cup sour cream, 1/3 cup heavy whipping cream, and 1 teaspoon vanilla extract. Mix until the batter is smooth and homogenous.
Pour the cheesecake batter into the prepared springform pan. Place the springform pan into the roasting pan in the oven.
Carefully pour the boiling water into the roasting pan until it reaches about 1 inch up the foil on the sides of the cheesecake pan.
Bake the cheesecake at 325°F for about 45 minutes, or until the edges are set and the center is no longer jiggly to the touch.
Remove the roasting pan from the oven, carefully lift the springform pan out of the water bath, and place the cheesecake on a wire rack. Let it cool at room temperature for at least 1 hour.
After it has cooled, place the cheesecake (still in its pan) into the freezer and freeze completely — several hours or overnight — until solid.
While the cheesecake is freezing, preheat the oven to 350°F and prepare two 9-inch round cake pans: spray with nonstick baking spray (spray with flour if available).
In a large bowl, whisk together 3 cups all-purpose flour, 2 cups granulated white sugar, 1 teaspoon baking soda, 1 teaspoon ground cinnamon, 1/2 teaspoon ground nutmeg, and 1/2 teaspoon salt.
In a separate bowl (or the same bowl after making a well), add 3 large eggs (room temperature), 3/4 cup vegetable or canola oil, and 2 teaspoons vanilla extract. Use an electric mixer to combine the wet ingredients with the dry ingredients on medium speed for 1 minute until well blended.
Scrape the sides of the bowl, then beat the batter on high speed for 1 minute.
Stir in 1 1/2 cups mashed ripe bananas and 1 cup chopped toasted pecans until evenly distributed.
Divide the batter evenly between the two prepared 9-inch pans and smooth the tops.
Bake the cake layers at 350°F for 25 to 28 minutes, or until a toothpick inserted into the centers comes out mostly clean.
Let the pans cool on a wire rack for 10 minutes. Then invert the cakes out of the pans onto the rack and let them cool completely.
Prepare the frosting: in a large bowl, using an electric mixer on medium-high speed, beat the remaining Two 8-ounce packages cream cheese (room temperature), 2 1/2 cups powdered sugar (sifted), 1/2 cup (1 stick) salted butter (room temperature), and 1 tablespoon vanilla extract until smooth and creamy. Do not overbeat.
Place one cooled cake layer on a cake plate or platter.
Remove the frozen cheesecake from the freezer. Release and remove the sides of the springform pan, slide a knife under the parchment to loosen the cheesecake from the pan, and peel off the parchment.
Compare the cheesecake round to the cake layers. If the cheesecake is slightly larger than the cake layers, trim the outer edge of the cheesecake gently on a cutting board so it matches the cake diameter.
Place the cheesecake layer on top of the first cake layer, then place the second cake layer on top of the cheesecake, aligning edges.
Apply a thin crumb coat of frosting: use a long, thin spatula to spread a thin, even layer of frosting over the top and sides of the stacked cake. Wipe the spatula clean each time before returning to the frosting bowl to avoid transferring crumbs.
Refrigerate the cake for 30 minutes to set the crumb coat.
Apply the final layer of frosting: place a large scoop of frosting on top, spread it evenly across the top, then spread it down the sides until smooth. Pipe or decorate additional frosting on top if desired.
Refrigerate the finished cake. Serve slices with sliced banana and a drizzle of caramel syrup. Keep leftover cake refrigerated.