In a large soup pot, heat 2 tablespoons of extra virgin olive oil over medium high heat. Add the onions and sauté, stirring until translucent and slightly golden, about 5 minutes. Add the corn, stir to mix. Add the vegetable broth and increase heat to high and bring to a boil.
Cover the pot and lower heat, simmer for 5 minutes. Add the cashew milk and salt and pepper. Stir and simmer for another minute. Turn off heat.
If the lobster tail is frozen, steam the lobster tail until the shell just turns red about 8 minutes.
Pre heat broiler. Place lobster tail on a baking sheet. With a kitchen shears, cut the top side of the lobster shell lengthwise. Pull apart shells slightly, season with salt and pepper. Broil for about 8 minutes or until lobster meat is opaque. Cool and remove tail from shell. Cut into bite size pieces.
In a mini food processor, process the basil leaves until finely chopped. Add 1/4 cup olive oil and process again to combine.
In a Vitamix or other powerful blender, puree the soup in batches. Return the mixture to the soup pot. Stirring and warm up over low heat.
Serve soup in bowls garnished with lobster meat and a drizzle of basil oil.