Whisk the gluten-free flour, brown sugar, baking powder, baking soda, pumpkin pie spice, and salt together in a large mixing bowl.
In a second bowl, whisk the milk, pumpkin puree, eggs, melted butter, and vanilla until smooth.
Pour the wet ingredients into the dry ingredients. Stir gently just until combined, some small lumps are fine. Let the batter rest 5 minutes so the flour hydrates.
Heat a 12-inch nonstick griddle or skillet over medium-low heat, about 350 F / 175 C. Brush lightly with butter.
Scoop 1/4 cup batter per pancake onto the griddle, leaving space between each. Cook 3 to 4 pancakes at a time so they aren't touching.
Cook for 2 to 3 minutes until bubbles form across the surface and the edges look dry and set.
Flip and cook the other side for 2 to 3 minutes until golden brown and the center springs back when pressed.
Transfer cooked pancakes to a plate, wipe the griddle, add a little more butter, and repeat with the remaining batter.
Serve warm, stacked, with maple syrup poured over the top.