Place 5 tablespoons unsalted butter in a medium microwave-safe bowl and microwave in 15-second bursts until melted, about 45 seconds total.

Coarsely chop ½ cup walnut pieces and halves. Add the walnuts, ½ cup all-purpose flour, ¼ cup packed light brown sugar, ¼ cup granulated sugar, 1 teaspoon ground cinnamon, ¼ teaspoon freshly grated or ground nutmeg, and ¼ teaspoon kosher salt to the butter. Stir with a fork until evenly moistened and a variety of crumb sizes form.

Refrigerate for at least 10 minutes while you make the cake batter.

Arrange a rack in the middle of the oven and heat the oven to 350°F. Line an 8-inch square baking pan with two overlapping sheets of parchment paper so that it hangs off all four sides and forms a sling.

Mash 2 very ripe medium bananas in a large bowl with a fork or potato masher until smooth (about ¾ cup). Add 1 large egg, ½ cup packed light brown sugar, ½ cup granulated sugar, ½ cup vegetable oil, ½ cup whole or 2% milk, 2 teaspoons vanilla extract, and ¼ teaspoon kosher salt. Whisk until combined.

Sprinkle evenly with 2 teaspoons baking powder. Add 1 ½ cups all-purpose flour and stir with a rubber spatula until just incorporated but no dry spots remain. Transfer the batter to the baking pan. Crumble the streusel evenly over the top.

Bake until the cake is browned and a tester inserted into the center comes out clean, 50 to 55 minutes. Place the pan on a wire rack and let cool for 15 minutes. Lift the cake out of the baking dish and place on the rack. Let cool for at least 1 hour more.

Transfer to a cutting board and cut into 12 pieces.