Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper.

In a large bowl, whisk together the self-rising flour and baking soda. Add the cold butter and cut it into the flour using a pastry blender until the mixture forms coarse crumbs (about 5–7 minutes). Create a well in the center and pour in the buttermilk. Mix with a fork until a shaggy dough begins to form.

Move the dough to a lightly floured surface and press it into a rough rectangle. Fold the dough into thirds using a bench scraper. Press it again into a rectangle, adding flour if it becomes sticky. Roll the dough with a rolling pin to about 1/2-inch thickness.

Sprinkle the dough with 1/4 cup cheese and 1/8 cup green onions. Fold the dough into thirds. Lightly dust with flour if needed and roll it out again to about 1/2-inch thickness. Sprinkle the remaining 1/4 cup cheese and 1/8 cup green onions on top. Fold into thirds again and roll out to about 1/2-inch thickness. Use a 2- or 3-inch round cutter to cut out 12 biscuits.

Place the biscuits onto the prepared baking sheet. Brush them lightly with buttermilk and sprinkle the tops with about 1 teaspoon cheese.

Bake in the preheated oven for about 20 minutes, or until the biscuits are fully cooked and golden brown. Transfer them to a wire rack to cool.