Cube chilled lobster lobster into quarter inch by quarter inch pieces. Melt 1/2 stick of butter over medium-low heat. Add sliced shallot, garlic, and cook until fragrant, about 5 minutes. simmer for another 5 minutes. Increase heat to medium. Add paprika; stir to blend. Add remaining 1/2 stick butter, 1 tablespoon at a time, stirring until melted and set aside. Combine wine, chopped shallot, and capers in saucepan. Boil over high heat until almost all liquid evaporates, about 1 minute. Remove from heat. Whisk yolks, lemon juice, and water in medium bowl. Place bowl over saucepan of barely simmering water. Whisk constantly until mixture is thick, about 3 minutes. Turn off heat. Whisk in lobster butter in 6 additions. Whisk in shallot mixture and tarragon. Season to taste with salt and pepper. Season with salt and pepper. Keep lobster sauce over warm water.
Preheat grill/broiler. Rub steaks with coarse kosher salt and pepper. Broil until cooked to desired doneness, about 6 minutes per side for medium-rare (5 minutes per side if boneless). Serve with lobster sauce.