Heat the olive oil in a heavy 4-quart saucepan over medium heat. When the oil is hot, add the green onions, Mexican mint marigold, mint, cayenne pepper and black pepper. Sauté, stirring often, until the onions are wilted—about 3 minutes.
Stir in the peas, add the chicken stock and bring the soup to a rolling boil. Reduce the heat, add kosher salt to taste and let the soup simmer for about 20 minutes, or until the peas are very tender.
Puree the soup in batches in a food processor or blender. Return the soup to a clean pot and cook for 30 minutes, or until the soup is slightly thickened. Stir in the heavy cream and cook just to heat through.
Serve hot, in rimmed soup bowls, with a tablespoon of sour cream in the center of each bowl. Toss the finely chopped cucumber with the ¼ teaspoon of salt, blending well. Scatter a portion over the sour cream and serve.