For the streusel topping, combine the flour, cold butter, light brown sugar, granulated sugar, salt, and cinnamon in a small mixing bowl. Use a fork or your fingers to cut the butter into the flour mixture until small pea-sized pieces form. Stir in the reserved diced apples. Place the streusel topping in the refrigerator until ready to use.
Preheat the oven to 425°F and position the oven rack in the middle. Line a muffin pan with 4 muffin liners.
In a medium bowl, whisk together the sour cream, pumpkin, apple juice, granulated sugar, light brown sugar, egg yolk, and vanilla extract until smooth and combined. Fold in the remaining diced apples.
In a small bowl, whisk together the flour, baking soda, salt, and pumpkin pie spice. Sprinkle the dry ingredients over the wet mixture and gently fold with a spatula until just combined and no dry streaks remain. Avoid overmixing to keep the muffins tender.
Divide the batter evenly among the prepared muffin liners. Sprinkle the chilled streusel topping evenly over each muffin.
Bake at 425°F for 5 minutes to allow the muffin tops to puff up. Reduce the oven temperature to 350°F and continue baking for 11 to 13 minutes or until a toothpick inserted in the center comes out mostly clean.
Let the muffins cool in the pan on a wire rack for 10 minutes before transferring them to the rack to cool completely.
Store the muffins covered at room temperature for 3 to 5 days.