Season steaks generously on all sides with salt and black pepper.
Heat olive oil in a heavy-bottomed skillet over medium-high heat until shimmering.
Sear steaks for 4 to 5 minutes per side for medium-rare (internal temperature of 130°F/54°C). Remove steaks from pan and allow to rest for 5 minutes.
Lower heat to medium and melt 1 tablespoon of butter in the same skillet.
Add shrimp to the skillet and sauté for 2 to 3 minutes until opaque and pink. Remove shrimp and set aside.
Add remaining tablespoon of butter and minced shallot to the pan. Sauté for 1 minute until translucent.
Deglaze the skillet with white wine, scraping the bottom to release fond. Reduce liquid by half.
Whisk in lobster stock and heavy cream. Simmer for 3 to 4 minutes until the sauce thickens and coats the back of a spoon.
Incorporate the cooked shrimp, lobster meat, and fresh tarragon into the sauce. Stir for 1 minute to heat through.
Plate the rested steaks and spoon the shrimp lobster sauce over each portion.