Fill a stockpot with water and a few heavy pinches of salt and bring to a boil over high heat. Add lobster tails and cook until bright red and beginning to curl up, 8-9 minutes.
Remove tails and cool. Once cool, cut each tail in half long-ways. Remove lobster meat from shells, chop and reserve for later use. Additionally, also reserve the lobster tail shells (we'll be stuffing the meat back in later on).
Heat a large pot like a dutch oven over medium. Add the butter and when melted, pour in the chopped mushrooms and cook until they become softer and begin to take on color, 6-8 minutes.
Add in cooked lobster tail meat, paprika, pepper and 1 tsp of salt and reduce the heat to low.
Pour in 1/2 cup of the heavy cream and 1 tbsp of the wine, stir to combine, and then simmer for 5 minutes, then remove from heat.
In a small bowl, whisk together the egg yolks with the remaining tbsp of white wine. Pour mixture into a small sauce pan and simmer, whisking constantly, until liquid thickens slightly and becomes a custard.
Remove from heat and slowly mix into lobster mixture.
Place reserved lobster shells on a parchment-lined baking sheet. Spoon lobster and sauce carefully into each shell. Save extra lobster sauce for serving.
Broil lobster tails until they begin to brown, 5-6 minutes.
Remove from oven and serve garnished with chopped Tarragon (if using), along side some toasted bread and a light salad.
