1. Preheat the oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners or homemade parchment liners cut into squares for better shape and easy removal.
2. Cut the butter into pieces and melt in a light-colored skillet over medium heat, stirring constantly. Cook until the butter foams and milk solids turn golden brown with a nutty, caramel-like fragrance (approximately 2-4 minutes). Remove immediately to prevent burning and pour into a bowl to cool for a few minutes but still warm.
3. Stir the granulated sugar and brown sugar into the warm browned butter until combined.
4. Add eggs, sour cream (or Greek yogurt), and vanilla extract to the butter mixture, mixing until even and smooth.
5. In a separate bowl, whisk together the flour, baking powder, baking soda, and salt.
6. Fold the dry ingredients into the wet mixture until just combined; some dry streaks or lumps are normal. Avoid overmixing to keep muffins tender.
7. Fold in the chocolate chips or chopped chocolate gently until distributed but batter remains thick and slightly lumpy.
8. For best texture, rest the batter for about 15 minutes to allow the flour to hydrate, which helps produce a softer, fluffier muffin.
9. Fill muffin cups about 2/3 to 3/4 full with batter. Almost filling the cups can help yield tall, rounded tops. Optionally, sprinkle the tops with coarse or turbinado sugar for a sweet crunch.
10. Bake muffins for 17 to 20 minutes until golden brown and a toothpick inserted in the center comes out clean or with moist crumbs. Alternatively, start baking at 425°F (220°C) for 7 minutes to encourage rise, then reduce to 350°F (175°C) for an additional 12-15 minutes.
11. Remove muffins from oven and cool in the pan for a few minutes before transferring to a wire rack to cool completely.