Stir the vinegar into the milk and set aside for 5 minutes, until it looks slightly thickened and curdled. This makes a quick homemade buttermilk that keeps the pancakes tender.
Melt 5 tbsp butter in a small saucepan over medium heat and keep swirling the pan for 4-5 minutes, until it foams, smells nutty and small golden brown bits form at the bottom.Pour the brown butter into a small bowl, scraping in all the brown bits, and let it cool for 5 minutes. This step gives the pancakes a rich, cookie-like flavor.
In a large bowl, whisk the flour, brown sugar, baking powder, baking soda and salt, breaking up any clumps of brown sugar.
Whisk the vanilla and cooled brown butter into the milk mixture. Pour it into the dry ingredients and fold until just combined, then gently fold in 1/2 cup of the chocolate chips. Let the batter rest for 10 minutes.
Heat a nonstick skillet or griddle over medium-low heat and grease it lightly with butter. Pour 1/4 cup of batter per pancake and sprinkle a few of the remaining chocolate chips on top of each.
Cook for 2-3 minutes, until bubbles appear on the surface and the edges look set, then flip and cook for 1-2 minutes more. Keep the heat moderate so the chocolate doesn't scorch on the pan.
Serve the pancakes warm and stacked, with a drizzle of maple syrup.