How to Make It
Cook pasta according to directions. Reserve 1 cup cooking liquid; drain.
While pasta cooks, melt butter in a large skillet over medium. Cook until butter is browned and very fragrant, 2 to 3 minutes. Add oil, garlic, anchovies, thyme, and pepper. Cook, stirring constantly, until anchovies dissolve and garlic begins to brown, about 1 minute. Add kale; cook, stirring often, just until wilted, 1 to 2 minutes. Add pasta, salt, and 2/3 cup reserved cooking liquid; toss to coat. If pasta seems dry, add additional cooking liquid, a splash at a time.
Divide pasta mixture among 4 shallow bowls. Top evenly with cheese, and serve with lemon wedges.