Rinse scallops and pat dry; sprinkle all over with salt and pepper. Heat oil in a 10- to 12-inch nonstick frying pan over medium-high heat. Add scallops and cook, turning once, until browned on both sides and opaque but still moist-looking in the center (cut to test), about 4 minutes total. Transfer scallops to a plate; cover with foil to keep warm.
Add 1/2 tablespoon butter, garlic, and shallot to pan. When butter is melted, add mushrooms; stir often until mushrooms are browned, about 5 minutes. Add remaining 2 tablespoons butter, along with chicken broth, parsley, tomatoes, white wine, and lemon juice; bring to a boil and cook 1 to 2 minutes.
Spoon potato purée into four shallow bowls; top each with 3 scallops. Spoon mushrooms and sauce over scallops.
Yukon Gold potato purée. In a 4- to 5-quart pan over high heat, bring 2 to 3 quarts water to a boil. Peel 1 pound Yukon Gold potatoes; cut into 1-inch chunks. Add potatoes to pan; cook until tender when pierced, 15 to 20 minutes. Drain and return to pan. Mash potatoes with 1/4 cup fat-skimmed chicken broth, 2 tablespoons whipping cream, and salt and pepper to taste.