Blend tarragon oil ingredients at high-speed in food processor. Set aside.
Sweat shallots in butter and oil.
Deglaze with wine, let reduce and add stock.
Let reduce further, add cream and whisk in cold butter.
Add lobster roe and tomalley. Let simmer for 5 minutes and strain.
Salt and pepper to taste. Set aside.
Rinse scallops and pat dry. Fry in very hot oil and butter.
Serve scallops in a ring on each plate with grilled vegetables in the middle. Garnish scallops with drizzles of lobster sauce and tarragon oil. (You may wish to filter the tarragon oil before serving.)