Melt the butter in a medium skillet over medium-high heat. Add the onion, garlic and peppers and cook until soft, about 4 to 6 minutes, stirring occasionally. Add the dill, season with salt and pepper. Put the mixture in the blender jar.
Add the avocado, and milk and 1 tablespoon of olive oil to the blender and puree. When completely smooth, transfer the puree to a bowl, cover, and refrigerate until chilled.
Heat the remaining 1 tablespoon of the olive oil in a medium skillet over medium-high heat. Add the shrimp and cook until curled, pink and opaque, about 2 to 4 minutes. To serve, pour the chilled soup into small glasses or bowls, add a few of the shrimp to each glass and garnish with the basil, sesame seeds, and a drizzle of oil.
*Cook's Note: We recommend Hass avocados for the smoothest avocado soupita.