Put a rack in the upper third of the oven and preheat oven to 375 degrees F. Line muffin pan with paper or foil liners
Melt butter in a small saucepan over medium heat. Keep an eye on the butter. Melt and cook down the butter until little brown bits appear in the pan. The crackling will subside and butter will begin to brown fairly quickly after that. Keep a close eye. (It does take a few minutes to brown butter, but make sure you don’t over cook it otherwise you’ll get black butter which will taste bitter) Remove from heat.
Whisk milk, egg, yolk, maple syrup, and vanilla until combined. Add the brown butter and stir to combine.
Whisk together flour, sugar, baking powder and salt in a medium bowl Add milk and butter mixture all at one and stir gently to combine.
Divide the batter among muffin cups and spread evenly.
Bake until golden and crisp and a wooden pick inserted into the center of a muffin comes out clean, about 18-20 minutes.
While the muffins are baking make the maple glaze.
In a small saucepan simmer maple syrup and lemon juice, stirring occasionally, until reduced to a thick (thicker than maple syrup) syrup. This will take about 15 minutes over a low flame.
Remove from heat and wait for the muffins to finish baking. When muffins are out of the oven and cool enough to handle, poke a few holes in the muffin top with a toothpick and dip each muffin top in the maple glaze. After dipping all twelve muffins, start with the first muffin you dipped and dip each muffin again.