Season the scallops with salt and pepper to taste and set aside at room temperature while you prepare the rest of the dish.

Melt the butter in a large pan over medium-high heat. When melted, add the shallots and cook, stirring often until soft and translucent, about 5 minutes. Add the mushrooms and a generous pinch of salt and continue cooking, stirring occasionally until the mushrooms release their liquid. Cook until no liquid remains and the mushrooms are beginning to brown, about 10 minutes. Add the white wine, if using, and cook until the liquid is reduced by half.

Nestle scallops into the simmering mushroom mixture and cook for about 2 minutes per side, until just lightly cooked. Transfer to a plate and set aside.

Strain the mushroom mixture through a fine mesh strainer, reserving all liquid. Do not clean the pan.

To the now empty pan, add the cream and cook over medium heat until reduced by half. Add back the liquid from the mushrooms as well as any juices that have accumulated on the scallop plate. Cook until slightly thickened. Remove from heat and let stand for a couple of minutes.

Add the egg yolk and stir quickly to ensure it is evenly mixed and does not have a chance to scramble. Stir in the zest and tarragon. Adjust seasoning to taste with salt and pepper, if desired.

Divide the mushroom mixture between 4 broiler-safe dishes. Top each dish with 3 scallops. Spoon the cream mixture over the scallops, allowing it to run into the mushrooms. Sprinkle with cheese and finally paprika, if using.

Broil the dishes until golden and bubbling hot. Serve immediately with fresh tarragon for garnish and lemon wedges.