Season both sides of tuna with salt and black pepper. In a large skillet, heat oil over medium-high heat. Add tuna to hot pan and cook 2 minutes per side, until golden brown.
In a medium bowl, combine broth, tomatoes, shallots, and tarragon. Add mixture to skillet and bring to a simmer. Simmer 2 minutes, until tuna is cooked to medium (or longer for more well done fish). Finish the sauce with butter. Serve 4 tuna fillets with all of the sauce and rice. Reserve the remaining tuna for melts, if desired.