Mix the dry ingredients: In the bowl of a stand mixer, combine 160g brown rice flour, 115g tapioca starch, 75g potato starch, 50g sugar, 8g salt, 7g instant yeast, 6g xanthan gum, and 8g baking powder. Whisk to combine evenly.
Make the psyllium gel: In a small bowl, whisk together 16g whole psyllium husk and 160g warm water until thickened into a gel. Set aside for about one minute to hydrate fully.
Combine the wet ingredients: In a medium bowl, whisk together 160g warm milk, 1 egg, 57g melted butter, and 5g apple cider vinegar. Add in the psyllium gel and whisk until smooth and uniform.
Make the dough: Pour the wet ingredients into the dry ingredients. Using the dough hook attachment, mix on medium speed for about 5 minutes, scraping the sides and bottom of the bowl as needed. The dough should be soft, thick, and slightly sticky.
Shape the rolls: Lightly oil your hands and divide the dough into 8–9 equal pieces (about 95–100 g each). Fold the edges of each piece over themselves toward the center to create a smooth top, pinch the seams closed, then flip seam-side down. Roll each piece under your hand in a loose claw shape until round and smooth. Arrange evenly in a greased 8×8-inch pan (3×3 grid for 9 rolls).
Proof the rolls: Cover the pan loosely and let rise in a warm spot (75–80°F) for about 45–60 minutes, or until puffy, nearly doubled, and just starting to touch.
Bake: Preheat the oven to 375°F (190°C). Brush the tops with 1 beaten egg for shine. Bake for 23–26 minutes, or until golden brown and the centers reach 195°F. Tent with foil during the last 5 minutes if browning too quickly.
Finish: While still warm, brush the tops with 28g (2 tablespoons) melted butter and sprinkle lightly with flaky sea salt. Let cool for a few minutes before serving.