In a small bowl, combine flour, cold butter, light brown sugar, granulated sugar, salt, and cinnamon. Use a fork or your fingers to mix until the mixture resembles coarse crumbs. Stir in a few reserved diced apples for added flavor, then place the bowl in the refrigerator to chill while you move on to the next steps.

Set your oven to preheat at 425°F (220°C). While the oven heats up, line a muffin pan with paper liners.

In a medium mixing bowl, whisk together the full-fat sour cream, pure canned pumpkin, apple juice, light brown sugar, granulated sugar, egg yolk, and vanilla extract until the mixture is completely smooth. Gently fold in the remaining diced apple cubes.

In a separate small bowl, whisk together the all-purpose flour, baking soda, salt, and pumpkin pie spice. Carefully add this dry mixture to the wet ingredients. Stir until just combined.

Spoon the muffin batter evenly into the prepared muffin liners, filling each about two-thirds full. Sprinkle the chilled streusel mixture generously on top of each muffin.

Place the muffin pan in the preheated oven and bake at 425°F for 5 minutes. Lower the temperature to 350°F (175°C) and continue baking for an additional 11 to 13 minutes until a toothpick comes out clean.

Let the muffins cool in the pan for about 10 minutes, then carefully remove them and place them on a wire rack to cool completely.