In a large bowl, combine 1 cup active sourdough starter, 2 cups warm water (95–105°F), 5 cups all-purpose flour, 2 tablespoons granulated sugar, and 2 teaspoons fine sea salt; mix until a shaggy dough forms, cover, and ferment at room temperature for 8–12 hours.
Sprinkle 1 teaspoon baking soda over the fermented dough and gently fold it in until evenly incorporated.
Lightly flour a work surface and turn out the dough; pat or roll to ½-inch thickness, then use a 3-inch cutter to cut out muffins, re-rolling scraps as needed.
Place muffins on a cornmeal-dusted baking sheet, sprinkle tops with extra cornmeal, cover loosely, and proof in a warm spot for 30–60 minutes until puffy.
Heat a cast-iron skillet or griddle over medium-low, melt 1 tablespoon unsalted butter, then cook muffins 5–7 minutes per side until golden brown and an internal temperature of 200°F is reached; add more butter as needed and cook remaining muffins.
Cool muffins on a wire rack, split each open with a fork, toast, and serve warm with butter, jam, or use for sandwiches.