Melt butter and oil in a nonstick pan over medium heat; saute the mushrooms for 5 to 8 minutes. Add in the shallots, salt, and black pepper. Turn heat to medium-high and cook, stirring often, until mushrooms are golden brown, about 6 minutes.
Pour white wine over mushroom mixture, dissolving any browned bits of food on bottom of the pan into the wine; bring to a simmer. Gently place scallops in and poach in the mushroom mixture until barely firm, about 2 minutes per side.
Using a slotted spoon transfer the scallops to a bowl. Using a slotted spoon transfer the mushrooms into another bowl. Keeping the leftover liquid in the pan. Pour any accumulated juices from the scallops into the pan and stir in the cream.
Bring to a rapid simmer and cook until cream is reduced in volume by about half, about 10 minutes. Stirring often. Until it is thick and creamy then remove from heat. Stir in chopped tarragon and lemon zest into sauce.
Spread the mushroom mixture into the bottom of a small baking dish, place the scallops on top of the mushrooms. Spoon cream sauce over scallops to coat; let sauce drizzle down into mushrooms. Top with Gruyere cheese and sprinkle lightly with paprika.
Turn oven's broiler to high.
Broil until sauce is bubbling and cheese is lightly browned, 5 to 6 minutes.
Portion and garnish with tarragon leaves.