For the beurre blanc: Heat the oil in a medium heavy-bottomed saucepan over medium heat. Add the shallots and sweat with a pinch salt until just softened, 1 to 2 minutes. Add the tomato paste and cook 1 to 2 minutes, stirring to combine. Add the wine and vinegar and simmer until the liquid is reduced to about 2 tablespoons, 3 to 4 minutes.
Add the cream (this will help stabilize your sauce and keep it from breaking) and simmer until reduced by one-third, 5 to 7 minutes. Strain the sauce into another warm saucepan over low heat. The sauce should remain warm, but never hot, or the sauce will break. On low or no heat, whisk in a few pieces of the butter at a time. Wait until each addition is incorporated before adding more butter. Once all of the butter is incorporated, add the lemon juice and combine. Set aside in a warm spot to hold. Just before serving, whisk in the white chocolate.
For the seared scallops: In a large cast-iron skillet, heat the oil over medium-high heat until it has a nice sheen and you can feel the heat coming off of the skillet. Dry your scallops well using paper towels, sprinkle each side with salt and pepper and add them to the hot skillet. Once the bottom of the scallops start to brown around the edges, add the butter to the skillet to help them caramelize. Let the butter melt, flip the scallops and cook until golden brown on each side and just cooked through, 2 to 3 minutes per side.
Toss some pea tendrils and tomatoes with the lemon juice and some olive oil, season with salt and pepper and serve with the scallops and beurre blanc.