Preheat the oven to 300°F. Grease an 8-inch round heavy aluminum pan (or two 6-inch round cake pans). Line the bottoms with parchment paper if desired and butter the parchment.
In a small bowl, combine 1 1/2 cups cookie crumbs and 3 tablespoons of the sugar. Stir to mix evenly.
Add the 5 tablespoons melted unsalted butter to the crumbs and stir until the crumbs are evenly moistened.
Press the crumb mixture firmly into the prepared pan(s), covering the bottom and pressing up the sides about three-quarters of the way.
In a food processor, combine the 1 pound cream cheese (not low-fat or whipped), 2/3 cup sugar, 1/2 cup mashed ripe banana, 1/4 cup sour cream, and 2 tablespoons flour. Pulse until smooth and well combined.
With the processor running, add the 4 eggs one at a time, pausing briefly between eggs. After all eggs are added, scrape down the sides of the bowl and pulse briefly so the mixture is uniform. This is your full cheesecake filling.
Measure out 1 1/4 cups of the filling and set it aside in a separate bowl. Pour the remaining filling into the prepared crust and smooth the top lightly.
Return 1 cup of the reserved 1 1/4 cups filling to the food processor. Add the 1 ounce melted unsweetened chocolate and pulse just until the chocolate is fully incorporated and the mixture is uniform (this becomes the chocolate swirl filling).
Drizzle the chocolate filling in abstract ribbons over the plain filling in the pan.
Drizzle the remaining 1/4 cup of reserved banana filling over the chocolate ribbons. Use a blunt knife or bamboo skewer to make a few swirls through the two fillings to create a marbled pattern; do not overmix.
Bake the cheesecake in the center of the oven for 45 minutes, or until the center is still slightly jiggly when the pan is gently shaken.
Remove the cheesecake from the oven and run a knife all the way around the edge between the cake and the pan to release it from the sides.
Return the cheesecake to the oven, turn the oven off, and let the cheesecake stand in the closed, turned-off oven for 15 minutes (do not open the door).
Remove the cheesecake from the oven and let it cool in the pan on a wire rack until it reaches room temperature. Then cover and refrigerate for at least 3 hours, or preferably overnight, to allow it to set completely.
To remove the cheesecake from the pan: wrap a flat plate or tray with plastic wrap and lightly spray the wrap with nonstick cooking spray if desired. Briefly hold the bottom of the cake pan over low heat until it is slightly warm (do not overheat). Gently shake the pan to help release the cheesecake. Place the greased plate over the top of the pan and quickly invert the pan so the cheesecake transfers to the plate. If desired, place the serving plate under the cheesecake and invert again so the cheesecake is right side up.
To make the strawberry sauce, place the 2 cups fresh strawberries and the remaining 3 tablespoons sugar in a blender or food processor and puree until smooth.
To serve, use a large chef’s knife dipped in hot water and wiped clean between cuts to slice the cheesecake. Drizzle with the strawberry sauce and garnish with whipped cream and chopped walnuts, if desired.