Preheat oven to 200°. Put a large frying pan (not nonstick) over medium-high heat. When hot to the touch, add 1 tsp. olive oil and sausages. Cover and cook 4 minutes. With tongs or a spatula, turn sausages over, cover, and cook until cooked through (cut one to test), about 4 minutes. Transfer sausages to a rimmed baking sheet, cover with foil, and put in oven to keep warm.
Add 1/3 cup wine or broth to the pan, using a wooden spoon or spatula to scrape up any browned bits left by the sausages. Add hominy, 1/4 tsp. salt, and 1/4 tsp. pepper. Cook, stirring occasionally, until all of the liquid has evaporated and hominy is hot and starting to stick to pan. Transfer hominy to baking sheet with sausages, piling it next to them. Add remaining wine or broth to pan, scrape up any browned bits, and pour over hominy. Re-cover baking sheet with foil and return it to oven.
Increase stovetop heat to high and add remaining 2 tsp. olive oil, the garlic slivers, chile flakes, and 1/8 tsp. salt to pan. Cook, stirring, until fragrant, about 30 seconds. Add spinach and cook, stirring, until wilted and cooked through. Divide spinach among 4 plates. Add hominy and sausage, plus more salt and pepper to taste. Serve hot.
Add cream: Skip step 2 and put hominy in a separate pan with 1 tbsp. butter, 3 tbsp. heavy cream, and salt and freshly ground black pepper to taste. Cook over medium heat, stirring occasionally, until hot, 5 to 7 minutes.
Swap greens: Use chard, kale, or other hearty greens in place of the spinach: Bring a large pot of water to a boil, add 10 oz. trimmed greens and 1 tbsp. salt, cook for 2 minutes, drain, and chop greens. Add instead of spinach in step
Try beans: Instead of hominy, use cooked white beans, pinto beans, or cranberry beans.
Go beyond sausage: We love the intense flavor this dish gets from sausage, but any quick-cooking meat works; try pork chops, chicken breast halves, or hanger steak.
Note: Nutritional analysis is per serving.