Heat oven to 375°F. Grease a 9×13-inch baking dish with a little butter.
Brown the sausage in a skillet over medium heat, breaking it up. Drain and let cool slightly.
Whisk flour, sugar, baking powder, baking soda, salt, and cinnamon in a large bowl.
In another bowl, whisk milk, beaten eggs, maple syrup, vanilla, and melted butter until smooth.
Pour wet mixture into dry. Stir just until combined; a few small lumps are fine.
Scatter the cooked sausage in the prepared dish. Sprinkle half the cheese over the top.
Pour the batter evenly over the sausage. Top with remaining cheese.
Bake 30–35 minutes until golden and set. Rest 10 minutes, then slice and serve.