In a medium bowl, combine the diced apples, bourbon, brown sugar, cinnamon, and salt. Toss gently to coat every piece of apple. Let this mixture sit for at least 15 minutes—during this time, the bourbon will infuse the apples and begin to break down their structure.
Preheat your oven to 375°F (190°C) and line a 12-cup muffin tin with paper liners or grease generously.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg until thoroughly combined.
In a separate large bowl, beat the softened butter with both sugars until light and fluffy, about 3 minutes with an electric mixer.
Add eggs one at a time, beating well after each addition. Stir in vanilla extract and sour cream until just combined.
Gradually fold the dry ingredient mixture into the wet ingredients, stirring just until combined.
Drain the bourbon-soaked apples, reserving the liquid for the glaze. Gently fold the soaked apples and ¾ cup of the chopped pecans into the batter.
Divide the batter evenly among the prepared muffin cups, filling each about ¾ full. Sprinkle the remaining ¼ cup of pecans on top of the muffins.
Bake for 22-25 minutes, or until a toothpick inserted into the center comes out clean or with just a few moist crumbs.
While the muffins are cooling, make the glaze by whisking together the powdered sugar, 2 tablespoons bourbon, and milk until smooth. For an extra boozy kick, add a tablespoon of the reserved bourbon soaking liquid.
Once muffins have cooled for 10 minutes, drizzle the bourbon glaze over the top of each muffin.