1. Bring 3 cups water to a boil in a stockpot. Place a vegetable steamer or rack in bottom of pan. Add lobster tails. Cover and steam for 8 minutes or until done.
2. Cool to room temperature.
3. Remove meat from shells (save shells); chop meat into bite-sized pieces.
4. Cover and chill.
5. Place lobster shells in a large zip-top plastic bag. Coarsely crush shells using a meat mallet or rolling pin.
6. Combine shells and milk in a small saucepan over medium heat. Bring to a simmer; cook 5 minutes (do not boil).
7. Remove from heat; cover and let stand 30 minutes.
8. Strain mixture through a fine mesh sieve into a bowl; discard solids. Set aside.
9. Preheat oven to 450°.
10. Heat oil in a large nonstick skillet over medium-high heat.
11. Add shallots; sauté 2 minutes or until soft.
12. Add mushrooms; sauté 4 minutes or until liquid begins to evaporate.
13. Stir in sherry, and cook 1 minute.
14. Combine reserved milk mixture, flour, black pepper, and white pepper in a small bowl; stir with a whisk until smooth.
15. Add milk mixture to pan; bring to a boil. Cook 1 minute or until thickened, stirring constantly.
16. Stir in basil and tarragon; cook for 1 minute, stirring occasionally.
17. Add reserved lobster meat, cream, and salt, stirring to combine.
18. Divide mixture evenly among each of 4 (1 1/2-cup) gratin dishes coated with cooking spray.
19. Combine cheese, panko, and melted butter in a small bowl; toss to combine.
20. Sprinkle 1/4 of the panko mixture over each gratin.
21. Bake for 12 minutes or until topping is browned.