Preheat the oven to 350℉. Line a 9 x 5-inch loaf pan with parchment paper and set aside.
Add the flour, baking powder, salt, cinnamon, and nutmeg to a large bowl. Whisk until evenly combined, then set aside.
Add the avocado oil, brown sugar, eggs, almond milk, and vanilla extract to a separate large mixing bowl and whisk to combine. Stir in the diced Granny Smith apples until evenly distributed.
Slowly add the flour mixture to the wet ingredients. Mix just until combined and no dry streaks remain; avoid overmixing so the loaf stays tender.
Add the softened cream cheese, brown sugar, and vanilla extract to a small bowl. Mix until smooth, then set aside.
Transfer half of the apple batter to the prepared loaf pan and spread it into an even layer. Spread the cream cheese mixture across the batter, then gently add and smooth the remaining batter over the filling.
Bake for 25 minutes, rotate the pan, and bake for another 25 minutes. The loaf is done when the top is set and a toothpick inserted into the bread portion comes out clean or with a few moist crumbs; avoid testing directly through the cream cheese stripe.
While the loaf cools, add the milk and powdered sugar to a small bowl and whisk until smooth. Pour the glaze over the loaf and let it set for 5 minutes; for the cleanest cream cheese stripe, allow the bread to cool completely before slicing.