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In a large bowl, whisk together ground oats, all-purpose flour, brown sugar, baking powder, baking soda, and salt. Set aside.
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In a separate bowl, whisk together milk, oil, vinegar, vanilla, and eggs.
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Make a well in the center on the dry ingredients, and slowly add the buttermilk mixture. Gently whisk until just incorporated, with a few lumps remaining. Do not overmix the batter.
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Heat a nonstick skillet over medium-high heat. Lightly grease the skillet, and pour batter in ¼ cup increments. Cook for a few minutes, until lightly browned and large bubbles appear. Flip the pancake and cook until browned on the second side. Repeat with remaining batter, brushing the pan with oil as needed.