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.