Whisk 1 cup rolled oats and 1 cup milk together in a large bowl. Let stand for 10 minutes for the oats to soften. Meanwhile, melt 1 tablespoon unsalted butter and set it aside to cool.

Add the butter, 2 eggs, and 1 tablespoon granulated sugar to the oats, and whisk to combine. Add ⅔ cup all-purpose flour, 2 teaspoons baking powder, ¼ teaspoon kosher salt, and ¼ teaspoon ground cinnamon, if desired, and whisk until just combined; do not overmix. Let stand for 5 minutes more. Meanwhile, heat a large cast iron or nonstick skillet over medium-high heat.

Add 1 teaspoon butter to the pan and swirl to coat. Drop the batter into the pan in 2-tablespoon portions, cooking 3 at a time. Cook until bubbles appear on the surface, the edges begin to look dry, and the bottoms are golden-brown, about 3 minutes. Flip the pancakes and cook until the other side is golden-brown, 2 to 3 minutes more.

Transfer the pancakes to a warm oven or plate. Repeat cooking the remaining batter, using 1 teaspoon butter for each batch.