Step 1

Cut 3 sticks of cold butter into 1/8-inch thick slices. Into a large bowl, sift flour, baking powder, salt, and baking soda. Add butter and toss to  coat. Add buttermilk and gently toss to blend, then press with your hands and turn mixture several times in bowl until flour absorbs most of buttermilk. Turn dough out onto a lightly-floured surface (it's OK if there are still some unincorporated dry ingredients).

Step 2

Using a floured rolling pin, roll dough into a ½-inch-thick rectangle. The dough will still be fairly shaggy. Fold dough into thirds, like folding a letter, and flip it over. Roll out dough again and repeat rolling and folding 3 more times, dusting work surface, dough, and rolling pin with flour as needed to prevent sticking. Roll out to a 3/4 -inch-thick rectangle.

Step 3

Using a 3 1/2-inch biscuit cutter, cut out biscuits, gathering and rolling scraps as needed until 10 to 11 biscuits are made. Transfer to a baking sheet. Brush tops generously with melted butter, then refrigerate for 20 minutes.

Step 4

Preheat oven to 400°F. Bake biscuits until tops are light brown and edges begin to darken, rotating baking sheet halfway through, about 16 minutes. Transfer biscuits to a wire rack and let cool completely.

Step 5

In a large skillet, melt butter with oil over medium-high heat. Add sausage and cook, stirring and breaking up sausage, until browned, about 5 minutes. Stir in flour, then garlic powder and onion. Cook, stirring often to prevent flour from sticking to bottom of pan, until flour is well-incorporated, a few minutes. Add milk and stir well, scraping up flour from bottom of pan and making sure flour is blended into milk. Season with salt and pepper and whisk until gravy thickens, reducing heat as needed to prevent bubbling over, about 5 minutes. Stir in half-and-half. Split biscuits in half. Place on plates, cut side up. Spoon gravy over, top with fried eggs, if using, and serve immediately.