Step 1: Preheat your oven to 375°F (190°C). Line a 12-cup muffin tin with paper liners or grease generously.
Step 2: In a large bowl, whisk together the all-purpose flour, granulated sugar, baking powder, and salt.
Step 3: In a separate medium bowl, whisk together the 3/4 cup milk, 1/4 cup melted butter, egg, and 1 teaspoon vanilla extract.
Step 4: Pour the wet ingredients into the dry ingredients. Stir gently with a spoon or spatula until just combined. Be careful not to overmix; a few lumps are fine.
Step 5: Prepare the cinnamon swirl: In a small bowl, combine the brown sugar, ground cinnamon, and 2 tablespoons melted butter. Mix until a thick paste forms.
Step 6: Spoon about half of the muffin batter into the prepared muffin liners, filling each about one-third full.
Step 7: Drop about 1/2 teaspoon of the cinnamon swirl mixture over the batter in each cup.
Step 8: Top with the remaining muffin batter, filling each cup about two-thirds full.
Step 9: Drop another small amount (about 1/4 teaspoon) of the cinnamon swirl mixture on top of each muffin. Use a toothpick or small knife to gently swirl the cinnamon mixture into the top layer of batter, creating a marble effect.
Step 10: Bake for 18-22 minutes, or until the tops are golden brown and a toothpick inserted into the center of a muffin comes out with moist crumbs (not wet batter).
Step 11: While the muffins are baking, prepare the glaze: In a small bowl, whisk together the powdered sugar, 2-3 tablespoons milk or cream, and 1/2 teaspoon vanilla extract until smooth and drizzly. Add more milk/cream if needed for desired consistency.
Step 12: Let the muffins cool in the tin for 5 minutes, then transfer them to a wire rack. Drizzle generously with the vanilla glaze while they are still slightly warm.