Cook the sausage: Heat a skillet over medium heat. Cook the sausage patties for about 3–4 minutes per side, or until browned and cooked through. Transfer to a paper towel–lined plate to drain any excess grease, then let cool slightly. The sausage should be fully cooked but still juicy inside.
Prepare the pancake batter: In a medium bowl, whisk together the flour, baking powder, sugar, and salt. In a separate bowl, combine the milk, egg, vanilla extract, and melted butter. Slowly pour the wet ingredients into the dry ingredients, whisking just until combined. The batter should be smooth and slightly thick — avoid overmixing to keep it fluffy.
Preheat the griddle or skillet: Heat a nonstick skillet or griddle over medium heat and lightly grease with butter or cooking spray. The surface should be hot enough that a drop of batter sizzles gently on contact.
Dip and cook the sausages: Using tongs, dip each cooked sausage patty into the pancake batter, coating it evenly. Place the dipped sausage carefully onto the hot skillet. Cook for 2–3 minutes on one side, until golden and bubbles form on the surface. Flip and cook for another 1–2 minutes on the other side until fully set and evenly browned.