Start by preheating your oven to 375°F and lining your muffin tin with paper liners or a light coat of nonstick spray. Getting the oven heating early means your batter won't sit around losing its rise. I always set my tin up before I even start mixing so everything moves quickly once the batter is ready.
In a large bowl, whisk together the flour, sugar, baking powder, and salt until evenly combined. This step distributes the baking powder so you don't end up with a muffin that rises unevenly. I like giving it an extra ten seconds of whisking just to be safe.
In a separate bowl, whisk the egg, milk, melted butter, and vanilla extract until smooth. Make sure your melted butter isn't piping hot, or it can start cooking the egg. I usually let mine cool for a minute or two on the counter first.
Pour the wet mixture into the dry ingredients and stir gently with a spatula until just combined. Overmixing is the enemy here, so stop as soon as you don't see dry flour streaks. A few small lumps in the batter are completely normal and actually a good sign.
Add dollops of your leftover cranberry sauce on top of the batter, then use a knife or skewer to swirl it through gently. I don't fully mix it in because those ribbons of cranberry are what make each bite special. If your sauce is jellied, give it a quick stir first so it swirls more easily.
Divide the batter evenly between the muffin cups, filling each about two-thirds full. Bake for 18 to 20 minutes, or until a toothpick inserted in the center comes out clean. Every oven runs a little differently, so I start checking around the 16-minute mark.
Let the muffins rest in the tin for five minutes before transferring them to a wire rack. This short rest keeps them from falling apart while they're still delicate and warm. Once cooled slightly, they're ready to enjoy with your favorite hot drink.