1. Heat the oil in a skillet over medium heat. Add the shallots and cook until they begin to soften, about 2 minutes.
2. Turn the heat to medium-high, add the mushrooms and sauté 2 minutes more.
3. Add the tomatoes, tarragon, salt and pepper. Heat thoroughly. If using canned tomatoes, simmer for 30 minutes to reduce the acidic taste.
4. Adjust the salt and pepper to taste. (This can be made ahead and kept in the refrigerator for up to 2 days.)
For the Grilled Flank Steak:
5. Generously season the steak with salt and pepper.
6. Preheat the grill.
7. Grill the flank steak for 4 to 8 minutes on each side, depending on the desired doneness. Let the steak rest on a carving plate for 1 or 2 minutes.
8. Slice the steak on the bias.
9. Serve a few slices of the steak with the mushroom ragout spooned over and around the slices.