In a medium pan over medium-low heat, add 6 tablespoons of the olive oil, lemon juice and tarragon, and season with salt and pepper. Gently cook for 3-4 minutes, occasionally stirring. Reduce the heat to low, add the crabmeat and cook for 1 minute longer. Remove from the heat and keep warm.

In a large cast-iron skillet or pan, heat the remaining 1 tablespoon olive oil. Add the radicchio, season with salt and pepper, and gently cook on both sides, for 4 minutes total.

Transfer the radicchio to a serving platter. Spoon the sauce and crabmeat over the top. Sprinkle with additional sea salt, if desired. Serve immediately.