Preheat oven to 350°F and line a muffin tray with liners. *See notes below on liners.
Make the Cinnamon Swirl Mix
Make the cinnamon swirl mix before you start the muffin batter so it has time to thicken slightly as the butter cools. Melt the butter in the microwave in 30-second increments.
3 tablespoon Butter
Add the dark brown sugar and cinnamon and mix everything together into a runny paste. Set aside while you make the muffin batter.
½ cup Dark Brown Sugar, 3 teaspoon Ground Cinnamon
Make the Muffin Batter
Whisk together the and eggs with the granulated sugar and light brown sugar - just until combined.
1 cup Granulated Sugar, 2 Eggs, ½ cup Light Brown Sugar
Add the wet ingredients and whisk together.
½ cup Vegetable Oil, 1 cup Milk, 1 teaspoon Vanilla Extract
Sift the dry ingredients into a bowl and then add to the batter - whisk until batter is smooth and free from lumps.
Fill each muffin case about ⅔ full of batter (or more for tulip cases - see notes).
Put the cinnamon mixture into a piping bag or freezer bag and snip a small hole in the end. Squeeze about 1 teaspoon of mixture onto each muffin and swirl it into the batter with a toothpick.
Add more muffin batter on top of each muffin - roughly 1-2 tablespoons.
Use the piping bag to squeeze a swirl of cinnamon mixture on top of each muffin - being careful not to let it touch the edges of the muffin cases.
Bake for 20 minutes or until a toothpick inserted in the middle comes out clean
Make the Glaze
Mix all the glaze ingredients together in a bowl until smooth and then drizzle over the cooled muffins
1 cup Icing Sugar, ¼ cup Cream Cheese, 2 tablespoon Milk, ½ teaspoon Vanilla Extract
Notes
Muffin Liners: For this recipe, I find I get the best results with the 'tulip' style muffin liners - the tall kind made of folded paper. If you don't have these you can either make your own by just folding some parchment paper squares into the muffin cups, or you can use regular muffin liners too - the recipe will still work great either way. If using the tulip liners you can fill the muffin liners with a lot more batter as they will rise higher, I recommend filling them to just above the top of the muffin pan (not the paper liner). You will get about 12 large muffins in tulip cases, or 18 - 24 smaller muffins in regular muffin cases.