Sprinkle about ½ teaspoon salt over the tuna steaks. Dredge each steak in the flour, coating both sides. Shake off the flour.
Pour 4 Tablespoons of olive oil into a large skillet and set it over medium-high heat. When the oil is hot, lay all the tuna in the pan, and sauté on the first side for about 1 minute, just until browned. Flip the steaks over, and brown the second side another minute or so. Take the pan off the heat. transfer the tuna to a platter and keep warm while you make the sauce.
Take the rehydrated porcini pieces from the soaking water and reserve the water. Pour the porcini water through a coffee filter or fine sieve to remove any sediment. Finely chop the porcini.
Pour 2 Tablespoons olive oil into the skillet, set it over medium-high heat, toss in the garlic cloves, then stir in the anchovy and the porcini. The anchovy will melt into the oil. Cook and stir until everything is sizzling nicely, then pour in the white wine, lemon juice, and porcini water. Add the thyme sprigs and season with the remaining salt. Bring the sauce to a boil. Cook until reduced by half.
When the sauce has thickened, arrange the tuna steaks in the skillet again, and pour in any juices from the platter. Heat for a minute in the bubbling sauce, then turn the steaks over and cook briefly on the second side The tuna should still be rare at this point.
Just before serving, drop the 2 Tablespoons butter into the pan in-between the tuna steaks, and stir it into the sauce. Turn off the heat and stir in the parsley.
Serve the steaks over pasta spooning sauce over them.