Remove lobster meat from shells and reserve shells for broth.

In a large pot, combine lobster shells and chicken broth. Bring to a boil, then simmer for 20 minutes to create a flavorful broth.

Strain the broth and return it to the pot.

Add coconut milk and bring to a simmer.

Whisk in chickpea flour, a teaspoon at a time, until the bisque reaches your desired consistency.

Return the blended mixture to the pot and add in the lobster chunks. Taste and adjust seasoning as needed.

Heat through and serve. Garnish with fresh thyme and a drizzle of olive oil.