Step 1Heat oven to 375 degrees.
Step 2In a food processor bowl, pulse together the flour, cornmeal, sugar, baking powder and salt. Add the cold cubed butter and pulse just until the mixture has the texture of lightly moistened cornmeal. There may be a few pea-sized chunks of butter remaining.
Step 3Pour in 3/4 cup whipping cream all at once and then pulse 4 to 6 times just to moisten the dough. Do not overmix or the dough will be tough.
Step 4Turn the dough out onto a lightly floured work surface and gather into a crumbly mass. Knead 3 to 4 times to make it cohesive and then pat into a rough circle 6 to 7 inches in diameter and a consistent 3/4 to 1 inch in height.
Step 5Using a sharp knife, cut the circle into 6 wedges. Transfer to a cookie sheet, brush with a little cream, and bake until risen and golden brown, 18 to 20 minutes. Turn the pan around halfway through to ensure even cooking. Remove to a cooling rack.
Step 1While the shortcakes are baking, melt the butter in a medium skillet over medium heat. Add the diced chorizo and cook until it begins to brown and crisp, about 3 minutes. Add the mushrooms and cook until they soften, about 5 minutes. Add the shallot and cook until it softens, about 3 minutes. Add the white wine and cook until it reduces to a syrupy glaze, about 5 minutes. Add the shrimp and toss them in the glaze. Add the cream and smoked paprika and simmer until the cream has reduced enough to lightly coat the back of a spoon, about 5 minutes. Season to taste with salt and freshly ground black pepper.
Step 2Split each shortcake in half horizontally. Place the bottom half on a plate and spoon the shrimp mixture over. Sprinkle lightly with minced green onion, place the shortcake tops on top and serve immediately.