Preheat oven to 350°F (175°C) and place rack in the center position.
Whisk together 1/4 cup flour, 1/4 cup brown sugar, and 1/2 teaspoon cinnamon. Cut in 2 tablespoons cold butter until coarse crumbs form. Chill until ready to use.
Grease a 9x5-inch loaf pan with butter or nonstick spray, then dust with 1 tablespoon flour, tapping out the excess.
Peel, core, and dice 2 medium apples into 1/2-inch pieces. Toss with 1 teaspoon lemon juice to prevent browning.
In a medium bowl, whisk together 2 cups flour, baking powder, baking soda, salt, 1 teaspoon cinnamon, and nutmeg.
Beat softened butter, granulated sugar, and 1/4 cup brown sugar on medium speed for 2-3 minutes until light and fluffy.
Beat in eggs one at a time, then add vanilla extract and mix until incorporated.
Alternate adding the buttermilk and dry ingredients in two additions each, mixing on low speed just until combined. Do not overmix.
Gently fold in the diced apples with a rubber spatula using 8-10 slow strokes.
Spread batter evenly into the prepared loaf pan. Sprinkle the streusel topping over the top and press down lightly.
Bake for 55-65 minutes, until a toothpick inserted in the center comes out clean. Tent with foil after 40 minutes if browning too fast.
Cool in the pan for 10 minutes, then run a knife around the edges and invert onto a cooling rack. Flip right-side up and cool completely, about 2 hours, before slicing.