In large, heavy bottomed pot, heat the extra-virgin oil. Add white onion and garlic and cook over medium heat until translucent, about 3 minutes. Add green tea, cream, Chardonnay and base. Cook over medium heat 30 minutes, stirring frequently. Do not let mixture boil.
Add matcha powder, green tea loose leaves and basil, then slowly stir in roux. Add tomato paste and cook at low temperature 30 to 40 minutes, or until mixture thickly coats the back of a spoon.
Just before serving, cut warm, cooked lobster meat into cubes and add to bisque.