Preheat a grill to medium-high heat.

Place chayote squash in a saucepan and cover with water.

Add 1/2 teaspoon salt to the water.

Bring to a boil and cook chayote until tender (about 25 minutes).

Drain the cooked chayote and cool slightly.

Peel the chayote and slice each in half. Pat dry.

Toss chayote with vegetable oil in a bowl.

Grill the chayote for 15 minutes, turning occasionally, until blistered and slightly charred.

Alternatively, heat a grill pan over high heat and cook chayote, in batches, 8 to 10 minutes, turning occasionally, or until slightly charred.

Remove charred chayote from heat, roughly chop, and set aside.

Heat butter in a stockpot over medium-high heat.

Add diced onions and cook until softened (about 3 minutes).

Add minced garlic and cook for 30 seconds, stirring.

Add the reserved chayotes, cumin, remaining salt, and pepper to the stockpot.

Stir in the chicken stock and bring the mixture to a boil.

Reduce heat to medium low and simmer for 20 minutes.

Remove from heat and puree the soup in batches until smooth.

Toss shrimp with Southwest seasoning and adobo sauce. Let stand for 5 minutes.

Return the soup to the stockpot and bring mixture to a boil.

Add the shrimp and cook for 2 minutes, or until cooked through.

Remove soup from the heat and stir in cilantro.

Prepare black bean relish: combine cooked black beans, red bell pepper, garlic, green onions, cilantro, lime juice, salt, and pepper in a bowl.

Adjust seasonings of the black bean relish with salt and pepper.

Refrigerate the relish for 30 minutes, stirring occasionally, before serving.

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