Preheat your oven to 350°F (175°C) and line a 12-cup muffin tin with paper liners or generously grease each cup.
In a medium bowl, beat the softened cream cheese until smooth and fluffy – about 2 minutes with an electric mixer. Add the sugar, egg yolk, vanilla extract, and lemon zest if using. Beat for another minute until well combined and silky. Transfer to a piping bag or zip-top bag with a corner snipped off. Place in the refrigerator while preparing the remaining components.
In a small bowl, whisk together flour, brown sugar, and cinnamon for the streusel. Using your fingertips or a pastry cutter, work the cold butter into the mixture until it resembles coarse crumbs. If using nuts, fold them in now. Set aside in the refrigerator.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg until evenly distributed.
In a separate bowl, whisk together the melted butter and brown sugar until well combined. Add the eggs one at a time, whisking well after each addition. Stir in the applesauce and vanilla extract until smooth.
Add the dry ingredients to the wet ingredients and gently fold together until just combined. Your batter should still have a few small streaks of flour. Gently fold in the diced apples, distributing them evenly throughout the batter.
Fill each muffin cup about ⅓ full with the apple batter. Remove your cream cheese filling from the refrigerator and pipe or spoon about 1 tablespoon into the center of each muffin. Top with the remaining batter, covering the cream cheese completely.
Sprinkle the streusel topping over each muffin, gently pressing it into the batter slightly. Bake for 22-25 minutes, or until a toothpick inserted into the muffin part (not the cream cheese) comes out clean.
Allow the muffins to cool in the tin for 5-10 minutes before transferring to a wire rack to cool completely.