Melt butter in a large skillet over medium heat; add shallots and sauté until translucent, 5 to 8 minutes. Stir in mushrooms, salt, and black pepper; increase heat to medium-high and cook, stirring often, until mushrooms are golden brown, about 10 minutes.

Pour wine into the pan and bring to a boil while scraping the browned bits of food off the bottom of the pan with a wooden spoon; bring to a simmer. Gently place scallops into wine and poach in the mushroom mixture until barely firm, about 2 minutes per side; transfer scallops to a bowl. Strain mushroom mixture into another bowl, reserving mushrooms and cooking liquid separately.

Return strained liquid to skillet, pour in any accumulated juices from scallops, and stir in cream. Bring to a boil and cook, stirring often, until cream sauce is reduced by about half, about 10 minutes. Turn off heat and let mixture cool for 1 minute.

Quickly whisk egg yolk into cream sauce until combined. Transfer skillet to a work surface (such as a heatproof countertop or cutting board) and stir 2 in teaspoons tarragon, lemon zest, and cayenne pepper.

Divide mushroom mixture into scallop shells, spreading it out to cover the bottoms of shells; place about 3 scallops onto each portion. Spoon cream sauce over scallops to coat; let sauce drizzle down into mushrooms. Sprinkle lightly with Gruyère cheese and paprika.

Preheat the oven's broiler. Slightly crinkle a large sheet of aluminum foil and place onto a baking sheet. Place filled shells onto foil and press lightly to help them stay level.

Broil in the preheated oven until bubbling and cheese is lightly browned, 5 to 6 minutes.

Transfer to serving plates lined with napkins to prevent shells from tipping; garnish each portion with 2 crossed tarragon leaves.