Temper the steaks at room temperature for 20 minutes; season all sides generously with salt and black pepper.
Heat olive oil and 1 tablespoon of butter in a heavy cast-iron skillet over medium-high heat until the butter foams and begins to brown.
Place steaks in the skillet and sear for 4 to 5 minutes per side for medium-rare (internal temperature of 130°F/54°C). Remove steaks from the pan and tent loosely with foil to rest.
Reduce heat to medium. Add the remaining tablespoon of butter to the same skillet. Add the shrimp and cook for 1.5 minutes per side until opaque and pink. Remove shrimp and set aside.
Add minced shallots to the skillet and sauté for 1 minute until translucent. Add garlic and cook for an additional 30 seconds until fragrant.
Deglaze the pan with white wine, scraping the bottom with a wooden spoon to release the fond. Simmer until the liquid is reduced by half.
Whisk in the heavy cream and lobster base. Bring to a gentle simmer and cook for 3 to 5 minutes until the sauce thickens enough to coat the back of a spoon.
Fold in the cooked lobster meat and the prepared shrimp, stirring for 1 minute to heat through.
Place each rested filet on a warmed plate. Spoon a generous amount of the lobster and shrimp cream sauce over the steaks.
Garnish with chopped tarragon and serve immediately.