Preheat your oven to 350°F (175°C) and grease a muffin tin or line it with paper liners.
In a large bowl, whisk together the flour, baking powder, salt, and sugar until well combined.
In another bowl, mix the milk, eggs, melted butter, maple syrup, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and stir until just combined. Do not overmix.
Divide the batter evenly among the muffin cups, filling each about halfway.
Place a cooked sausage patty on top of the batter in each muffin cup, then add a slice of cheese on top of the sausage.
Spoon a little more batter over the sausage and cheese until the muffin cups are about 3/4 full.
Bake in the preheated oven for 18-20 minutes, or until a toothpick inserted into the center comes out clean.
Allow the muffins to cool in the pan for 5 minutes before transferring them to a wire rack to cool completely.