Heat oil in a large stock pot over medium heat. Saute onion, shallots, garlic and 1 thinly sliced Serrano chile until soft, 8 minutes.
Purée tomatillos in a blender until smooth.
Add half of tomatillo purée to stock pot and cook, stirring often, until thickened, about 5 minutes. Season with salt and pepper. Add 1 cup cilantro to remaining tomatillo purée in blender and blend until smooth; set aside.
Add hominy, chicken stock and Tabasco Green Pepper Sauce to pot. Bring to a simmer and gently cook over medium-low for 5 minutes. Add shrimp and simmer for 2-3 minutes. Remove from heat. Stir in reserved raw tomatillo-cilantro purée, season with salt and pepper.
Divide stew among bowls and top with radishes and remaining chile. Serve with lime wedges.
Frozen cooked shrimp may be substituted for fresh. Add thawed shrimp to the soup 3 minutes before cooking is complete, or if still frozen, cook for 5-6 minutes.
Recipe adapted from Chris Morocco's recipe for Green Posole With Cod And Cilantro in Bon Appetit.