In a large bowl, whisk together the self-rising flour, pumpkin pie spice, and salt.
In a medium bowl, whisk together the buttermilk, pumpkin, brown sugar, melted butter, vanilla extract, and eggs.
Make a well in the center of the flour mixture. Add the wet ingredients to the dry ingredients; stir just until combined. Let the batter rest for about 10 minutes, which will give it time to thicken and allow the flour to hydrate.
Place a skillet or griddle over medium heat. When the skillet is hot, coat or brush with oil. Working in batches, measure ⅓ cup of batter for each pancake. Spread batter, if necessary, so that each pancake is at least 4 inches in diameter. You want them thick, but if they're too thick, they may be dense or undercooked in the center.
Cook until bubbles form on top, about 2 ½ - 3 minutes per side. If the pancakes start to get too dark before the inside is cooked through, reduce the heat to medium-low or low. The pancakes need at least 2-3 minutes per side to fully cook through.
Transfer the pancakes to a baking sheet and place in a 200ºF oven to keep warm, if desired. Repeat cooking the remaining batter, adding more oil to the pan as needed. Serve with apple cider syrup or maple syrup.