Bring a large pot of cold water to a boil over high heat. Meanwhile, pull off scallops' connective muscle (the opaque white flap attached to side of scallop) and put scallops into a medium saucepan. Add onions, tarragon, 1 tsp. of the oil, and salt and pepper to taste. Cut off 2" from base end of chives and add to saucepan. Finely chop the remaining chives and set aside. Put saucepan over medium heat and cook mixture until onions begin to soften, about 5 minutes. Add wine and bring to a boil. Reduce heat to low and gently simmer until onions are soft, about 10 minutes. Add 2 generous pinches salt to the boiling water, add pasta, and cook, stirring frequently, until just tender, 1–5 minutes, depending on type of pasta. Drain pasta and set aside.
Heat a large cast-iron or other heavy skillet over medium-high heat. Season scallops to taste with salt and pepper. Add the remaining 1⁄2 tsp. oil to skillet, then add scallops and sear each side until golden brown, about 2 minutes per side. Transfer scallops to a warm plate, loosely cover with foil, and set aside.
Return skillet to medium-high heat. Strain wine and onion mixture into skillet, discarding solids, and cook, scraping browned bits stuck to bottom of skillet with a wooden spoon, for 1–2 minutes. Add pasta, cream, butter, and lemon zest and juice; season to taste with salt and pepper and cook, stirring and tossing pasta in sauce, until sauce has thickened and been absorbed by pasta, 1-2 minutes.
Arrange 3 scallops on each of 4 warm plates, then divide pasta between plates and garnish with chopped chives.