01 - In a small saucepan, melt 1/4 cup unsalted butter over medium heat, swirling occasionally until the butter foams and turns golden brown with a nutty aroma. Remove from heat and allow to cool slightly.
02 - In a large mixing bowl, combine flour, granulated sugar, baking powder, baking soda, and salt. In a separate bowl, whisk together the whole milk, eggs, cooled brown butter, and vanilla extract. Add wet ingredients to dry and gently mix just until incorporated; a few lumps are acceptable.
03 - Stir melted butter, light brown sugar, and ground cinnamon together until smooth. Transfer to a piping or zip-top bag and snip a small opening at one corner.
04 - Melt 2 tablespoons unsalted butter in a medium saucepan over medium heat. Add diced apples, brown sugar, ground cinnamon, nutmeg, lemon juice, and a pinch of salt. Stir frequently and cook until apples are soft and the mixture is thickened, about 8–10 minutes. Remove from heat and keep warm.
05 - Heat a nonstick skillet or griddle over medium-low and lightly grease. Ladle 1/4 cup batter for each pancake onto the surface. When bubbles start to appear, pipe a cinnamon swirl onto each pancake. Cook until the edges are set, about 2 minutes, then flip carefully. Cook another 1–2 minutes until golden and cooked through.
06 - Stack pancakes on serving plates. Spoon warm apple compote generously over the top. Optionally dust with powdered sugar or drizzle with maple syrup to finish.