1. Make the relish:In a saucepan over medium-high heat, warm oil and add shallots and ginger. Reduce heat to medium. Cook, stirring often, until softened, about 3 minutes. Add p remaining ingredients. Cook until liquid is reduced and syrupy, about 10 minutes. Remove from heat and let stand for 20 minutes. Makes 1 cup.
2. Make the biscuits:In a large bowl, whisk together flour, cornmeal, baking powder, baking soda, salt, and pepper. Work shortening into flour mixture by breaking up chunks with your fingertips until only small pea-sized pieces remain. Add in a few slices of chilled butter and coat in flour. Press the pieces between well-floured fingertips into flat (nickel-size) pieces. Repeat until all chilled butter is incorporated. Place bowl in freezer until chilled, 15 minutes.
3. Preheat oven to 450 degrees. Remove bowl from freezer and gently stir buttermilk into flour mixture with a fork. Add thyme. Stir until dough forms a ball and no dry bits of flour remain. (The dough will be sticky and shaggy.) Turn the dough out onto a floured surface. With floured hands, pat it to a ¼-inch-thick, 10-inch rectangle. Add more flour if needed to prevent sticking. Fold dough into thirds using a bench scraper or metal spatula. Lift the short end of the dough and fold in thirds again. Rotate dough 90 degrees, dusting the work surface underneath with flour. Roll and fold again into a 10-inch square about ½-inch thick. Using a 2-inch round floured cutter, cut out 12 biscuits. Place 1 inch apart on an ungreased baking sheet. Brush biscuit tops with melted butter. Bake until the tops are golden brown, about 15 minutes.
4. Make the sausage:In a large bowl, stir together pork with remaining ingredients; let stand 15 minutes. Scoop about ¼ -cup of the mixture onto a wax paper-lined baking sheet, and shape into a ½-inch-thickpatty. Repeat until the mixture is gone. In a cast-iron skillet over medium-high heat, brown patties in batches until golden brown about 4 minutes per side.
5. To assemble: Split the biscuits. Top the bottom half of the biscuits with sausage patty and relish. Cover with top halves.