Preheat a grill to medium-high heat.

Place chayote squash into a medium saucepan, with enough water to cover. Add 1/2 teaspoon salt. Bring to a boil, and cook until tender, about 25 minutes. Drain and cool slightly. Using a vegetable peeler or pairing knife, remove the peel from the chayote, slice each chayote in half, and pat dry. In a medium bowl, toss the chayote with the vegetable oil.

Arrange chayote on the preheated grill, 5 to 6 inches from the top of the coals. Cook, turning occasionally, until blistered and slightly charred, about 15 minutes. Alternately heat a grill pan over high heat and cook chayote, in batches, 8 to 10 minutes, turning occasionally, or until slightly charred. Remove from the heat, roughly chop, and set aside.

Heat the butter over medium-high heat in a medium stockpot or soup pot. Add the onions and cook until softened, about 3 minutes. Add the garlic and cook, stirring, 30 seconds. Add the reserved chayotes, cumin, remaining salt, and the pepper to the stockpot. Stir in the chicken stock and bring the mixture to a boil. Turn the heat down to medium low and simmer for 20 minutes. Remove from the heat and, in small batches, puree the soup in a blender or food processor until smooth.

Toss the shrimp with the Southwest seasoning and the adobo sauce and let stand for 5 minutes. Meanwhile, return the soup to the stockpot and bring mixture to a boil.

Add the shrimp and cook for 2 minutes, or until the shrimp are cooked through. Remove the soup from the heat and stir in the cilantro.

Serve immediately, garnishing hot soup with Black Bean Relish and sour cream