Banana Chocolate Beignets

Name: Banana Chocolate Beignets
Ingredients: 1/2 cup whole milk; 1/2 cup water; 1 cup whole milk; 1/2 vanilla bean; 3 large egg yolks; 1/3 cup sugar; 2 tablespoons cornstarch; Butter for glossing; 2 large bananas; 1/4 cup sugar; 1 tablespoon unsalted butter; 3 tablespoons heavy cream; 1 large egg beaten with 1 teaspoon cold water for egg wash; 3 ounces unsalted butter; 2 tablespoons sugar; 1 1/2 tablespoons unsweetened cocoa powder; 1 teaspoon cinnamon; 1/4 teaspoon salt; 1 1/2 cups all-purpose flour; 6 large eggs at room temperature; 2/3 cup all-purpose flour for kneading; 2 cups heavy cream; 4 ounces unsalted butter cut into pieces; 1/2 cup sugar; 1/2 cup toasted walnuts finely ground; 1 tablespoon walnut oil (optional); Pinch of salt; Canola or vegetable oil for frying; Confectioner's sugar; Melted semisweet chocolate (optional)