Preheat oven to 400 degrees F (200 degrees C). Line a baking sheet with parchment paper.
Whisk self-rising flour and baking soda together in a mixing bowl. Add cold butter and cut it into flour with a pastry blender until texture resembles coarse crumbs, 5 to 7 minutes. Make a well in the center of the flour mixture and pour in the buttermilk. Stir with a fork just until mixture starts to come together to form a shaggy dough.
Transfer dough to a floured work surface. Press into a roughly shaped rectangle. Fold into thirds using a bench scraper. Press again into a rectangle. Flour surface if the dough seems sticky. Roll dough with a rolling pin to 1/2-inch thickness. Sprinkle with half of the shredded cheese and half of the green onions. Fold dough into thirds. Dust with flour, if necessary, and roll out again to about 1/2-inch thickness. Top with remaining cheese and green onions. Fold into thirds and roll out again to about 1/2 inch thickness. Cut biscuits with a 2- or 3-inch biscuit cutter.
Transfer biscuits to prepared baking sheet. Brush lightly with buttermilk. Sprinkle tops with about a teaspoon of grated cheese.
Bake in preheated oven until cooked through and golden brown, about 20 minutes. Transfer to a rack to cool.
