In a medium bowl, whisk together the milk, vinegar (or lemon juice), and vanilla. Let sit for 5 minutes until slightly thickened.
In a large bowl, whisk the flour, brown sugar, baking powder, and salt. Break up any clumps of sugar so it blends evenly.
Pour the wet mixture into the dry ingredients, add the melted butter, and whisk gently until just combined. A few lumps are fine. If the batter feels too thick and heavy (sticks to the whisk in clumps), add 1–2 tbsp extra milk to loosen it. If it feels too thin and runny, sprinkle in 1–2 tbsp extra flour. The goal is a thick but pourable batter.
Place a nonstick skillet or griddle over medium to medium-low heat. Brown sugar caramelizes quickly, so high heat will give you pancakes that look done on the outside but are raw in the middle.
Lightly coat the pan with oil or butter. Pour about ½ cup batter per pancake onto the hot surface. Cook 2–3 minutes, until bubbles form on top and edges look set. Flip and cook another 1–2 minutes, until golden and cooked through. If your pancakes are browning too fast, lower the heat and give them more time. If they’re spreading too thin, stir in a spoonful of flour.
Stack the pancakes and serve warm. They’re sweet enough to eat plain, but butter and syrup bring out the caramel notes, and fruit or nuts add contrast. For a dessert-style stack, drizzle with caramel sauce and finish with a scoop of ice cream.