To make the ragout, melt the butter with the oil in a large skillet over medium heat. Add the garlic and cook stirring often, until garlic gives off its aroma, about 1 minute. Add the mushrooms and cook, stirring occasionally, until they give off their juices, about 4 minutes. Stir in the sugar snap peas and cook for 1 minute. Add the tomatoes, broth, lemon juice, and tarragon. Bring the broth to a simmer. Cook stirring often, until the tomatoes are heated through, about 3 minutes. Remove from the heat, partially cover with a lid, and keep warm.

Meanwhile, heat a non-stick skillet with the olive oil, sprinkle with the tarragon, and season with salt and pepper. Place the salmon, flesh side down and cook 4 minutes over medium heat until lightly crisped. Turn and continue cooking until the fish is opaque in the center with a tinge of rose color when prodded with the tip of a sharp knife. Remove from pan and keep warm.

Add the remaining 2 tablespoons chilled butter, cut into bits, to the vegetables. Stir with a wooden spoon, being careful not to break up the vegetables, to melt the butter. Season the vegetables with salt and pepper and divide onto 4 dinner plates. Place the salmon on top and serve immediately.