Toast the pecans. Preheat oven to 350°F (175°C). Spread all pecans on a rimmed baking sheet. Toast for 6–8 minutes until fragrant and golden. Cool completely. Roughly chop 1 cup for the batter and finely chop ½ cup for the topping.
Prep the pan. Butter and flour a 9×13-inch baking pan or line with parchment paper, leaving overhangs on both long sides.
Mix the dry ingredients. In a large bowl, whisk together flour, baking soda, baking powder, salt, cinnamon, and nutmeg. Set aside.
Cream butter and sugars. In a stand mixer with paddle attachment, beat softened butter, oil, granulated sugar, and brown sugar on medium speed for 3 minutes until pale and fluffy.
Add eggs and bananas. Add eggs one at a time, beating well after each. Mix in vanilla extract, then mashed bananas. Batter may look slightly curdled — that's normal.
Alternate flour and buttermilk. With mixer on low, add flour in 3 additions alternating with buttermilk in 2 additions, starting and ending with flour. Mix until just combined. Fold in 1 cup toasted pecans by hand with a spatula.
Bake. Pour into prepared pan and smooth the top. Bake at 350°F (175°C) for 35–40 minutes, until a toothpick inserted in the center comes out with a few moist crumbs. Cool on a wire rack for 15 minutes.
Brown the butter. In a light-colored saucepan over medium heat, melt ½ cup butter. Cook, swirling occasionally, until golden-brown specks appear on the bottom and the butter smells nutty, about 4–5 minutes. Remove from heat immediately.
Make the glaze. Add brown sugar and milk or cream to the browned butter. Return to medium heat, bring to a gentle simmer, and whisk constantly for 1 minute. Remove from heat, stir in vanilla, then whisk in sifted powdered sugar until completely smooth and glossy.
Glaze and finish. Pour warm glaze immediately over the warm cake. Spread quickly to the edges. Scatter finely chopped toasted pecans over the top before the glaze sets. Rest for 30 minutes before slicing into squares.