Heat 2 Tbsp. extra-virgin olive oil and 2 Tbsp. unsalted butter in a large high-sided skillet over medium-high. Add 2 large onions, thinly sliced; season with kosher salt. Cook, stirring often, until onions are softened and brown around the edges, 10–14 minutes.
Add 4 garlic cloves, thinly sliced, to skillet with onions and cook, stirring constantly, until softened and fragrant, about 1 minute. Add 1 Tbsp. white miso and cook, stirring constantly, until browned and beginning to stick to bottom of pan, 1–2 minutes. Pour in 1 cup low-sodium beef or chicken broth or water, scraping up any browned bits stuck to bottom of pan, and cook, stirring, until miso is dissolved, about 2 minutes. Season generously with freshly ground pepper. Reduce heat to low and keep onion mixture warm until pasta is ready.
Meanwhile, cook 12 oz. spaghetti in a large pot of boiling salted water, stirring occasionally, until very al dente, about 1 minute less than package directions.
Using tongs, transfer pasta to skillet (a little water coming along is okay). Increase heat to medium and add 2½ oz. Parmesan, finely grated, remaining 1 Tbsp. unsalted butter, and ½ cup pasta cooking liquid. Cook, tossing often and adding more pasta cooking liquid by ¼-cupful as needed, until cheese is melted and sauce clings to pasta, about 2 minutes.
Divide pasta among bowls and top with ¼ cup 1½”-long chives and more finely grated Parmesan; season with pepper.