In a large bowl, mash the bananas thoroughly with a fork until mostly smooth with just a few small lumps. You want about 1 cup mashed. Whisk in the eggs, milk, and vanilla until combined.

In a separate bowl, whisk together the gluten-free flour, baking powder, cinnamon, and salt. This prevents clumps of baking powder in your pancakes.

Pour the dry ingredients into the wet. Stir with a rubber spatula until just combined. The batter will be thick and slightly lumpy. Do not overmix. Let rest for 5 minutes while you heat the pan.

Heat a large nonstick skillet or griddle over medium-low heat for 3-4 minutes. Add a small pat of butter and spread to coat. The pan is ready when a drop of water sizzles gently.

Scoop batter by heaping 1/4 cupfuls onto the skillet, spacing 2 inches apart. Cook until edges look set and small bubbles form across the surface, about 2-3 minutes. The bottoms should be deep golden brown.

Flip gently with a thin spatula. Cook until the second side is golden and the pancake feels firm when pressed lightly in the center, about 2 minutes more. Transfer to a warm plate and repeat with remaining batter, adding more butter as needed.