For the berry compote (optional): Place all of the ingredients in a medium saucepan, stir to combine, and bring to a boil over medium heat. Reduce the heat to low and simmer, stirring occasionally, until the compote has thickened, about 1 hour. Remove from heat and let cool slightly. For the pancakes: Sift the tapioca flour, sorghum flour, oat flour, teff flour, sugar, baking powder, xanthan gum, salt, and guar gum into a large bowl, discarding any coarse bits left in the sifter; set aside. Whisk the milk, eggs, and vanilla together in a medium bowl until the eggs are broken up and the mixture is evenly combined. Add the melted butter and whisk to incorporate. Make a well in the center of the flour mixture, pour in the milk mixture, and stir with a rubber spatula until just combined. If you’re using the berry compote, scoop a few tablespoons into the pancake batter and stir to evenly incorporate. Let the batter stand at room temperature for at least 1 hour before cooking. (Preferably, let the batter rest overnight in the refrigerator.) Heat a large nonstick frying pan or griddle or a seasoned cast iron skillet over medium heat until hot, about 4 minutes. Test to see if the pan is hot enough by sprinkling a couple of drops of cold water in it: If the water bounces and sputters, the pan is ready to use. Once the pan is ready, use a paper towel to rub it with a thin coating of vegetable oil. Ladle the pancake batter by the 1/4 cup into the pan. Cook the pancakes undisturbed until the bottoms are lightly golden brown, about 3 to 4 minutes. Carefully flip the pancakes, give each a gentle press with the spatula to slightly flatten, and cook until the bottoms are golden brown, about 3 to 4 minutes more. Flip the pancakes one more time and cook until they’re no longer wet in the center, about 3 to 4 minutes more. Remove to a plate and repeat with the remaining batter. Serve with the berry compote, if using.
