Preheat your oven to 350°F (175°C) and position a rack in the center. Grease a 9x5-inch loaf pan and line with parchment paper, leaving an overhang on the sides for easy removal.
In a medium bowl, whisk together the flour, brown sugar, granulated sugar, cinnamon, and salt for the streusel. Add the cold cubed butter and use your fingers or a pastry cutter to work it into the dry ingredients until the mixture resembles coarse crumbs with some pea-sized pieces remaining. Fold in the nuts if using, then refrigerate while preparing the bread batter.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg until well combined.
In a separate large bowl, beat the softened butter and brown sugar with an electric mixer on medium speed until light and fluffy, about 3-4 minutes.
Add eggs one at a time, beating well after each addition. Stir in the vanilla extract, milk, and Greek yogurt until just combined.
Gradually fold the dry ingredients into the wet mixture, stirring just until no flour streaks remain. Be careful not to overmix.
Gently fold in the diced apples, being careful not to overmix. For distinct apple pieces throughout your bread, dice half your apples finely and the other half in slightly larger chunks.
Pour the batter into the prepared loaf pan and spread evenly. Remove the streusel topping from the refrigerator and crumble it evenly over the batter, gently pressing it in just slightly so it adheres during baking.
Bake for 55-65 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs (not wet batter). If the streusel begins to brown too quickly, loosely cover with aluminum foil after about 40 minutes.
Allow the bread to cool in the pan for 15-20 minutes before lifting it out using the parchment paper handles. Transfer to a wire rack to cool completely before slicing.