Preheat the oven to 300°F. Grease an 8-inch round heavy aluminum pan (or two 6-inch round cake pans). If using parchment, line the bottom and grease the parchment.
In a small bowl, combine the cookie crumbs and 3 tablespoons of the sugar. Stir in the melted butter until the crumbs are evenly moistened.
Press the crumb mixture firmly into the bottom of the prepared pan and up the sides about three-quarters of the way. Set the crust aside.
In a food processor, place the cream cheese, 2/3 cup sugar, mashed banana, sour cream, and flour. Pulse until smooth.
With the processor running, add the eggs one at a time, pausing to scrape down the sides of the bowl as needed and pulsing briefly after each addition so the mixture is homogeneous but not overmixed.
Measure out 1 1/4 cups of the plain filling into a separate bowl and set it aside. Pour the remaining plain filling into the prepared crust and smooth the top.
Return 1 cup of the reserved plain filling to the food processor. Add the melted unsweetened chocolate and pulse just until the chocolate is evenly incorporated.
Spoon or drizzle the chocolate filling in an abstract ribbon pattern over the top of the plain filling in the pan.
Drizzle the remaining 1/4 cup of plain filling over the chocolate ribbons. Use a blunt knife or a bamboo skewer to gently swirl the two fillings to create a marbled pattern; do not overmix.
Bake on the center rack for 45 minutes, or until the edges are set and the center is still just slightly jiggly.
Remove the cheesecake from the oven and run a thin knife all the way around the edges to release the cake from the pan. Return the cheesecake to the oven, turn the heat off, and let it stand in the closed oven (do not open the door) for 15 minutes.
Remove the cheesecake from the oven and let it cool in the pan on a rack until it reaches room temperature. Then cover and refrigerate for at least 3 hours, or overnight, to set completely.
To unmold: if you used parchment, lift the cheesecake out by the parchment and transfer it to a serving plate. If not using parchment, run a thin knife around the edge again, place a serving plate over the top of the pan, invert quickly, and lift the pan off. If it sticks, loosen again with the knife and repeat.
Meanwhile, 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. Refrigerate until ready to serve.
To cut slices, dip a large chef’s knife in hot water, wipe it dry, and make the cut. Wipe the knife clean and re-dip in hot water between cuts for clean slices.
Serve slices drizzled with strawberry sauce and, if desired, garnish with whipped cream and chopped walnuts.