Toast the breadcrumbs: Warm 2 tbsp of the olive oil in a large skillet over medium heat. Add the breadcrumbs and cook, stirring often, until deep golden and crisp, 3β5 minutes. Transfer to a bowl and set aside.
Bring 4 quarts of water to a boil in a large pot. Add the kosher salt.
Build the sauce base: In the same skillet, add the remaining 4 tbsp olive oil, garlic, and red pepper flakes. Cook over medium-low heat until the garlic is fragrant and just turning pale gold, 2β3 minutes. Add the anchovies and mash until dissolved, 1β2 minutes. Remove from heat so the garlic doesnβt brown while the pasta cooks.
Cook the greens and pasta together: Add the broccoli rabe stems and larger pieces to the boiling water and cook 2 minutes. Add the remaining leaves/florets along with the orecchiette. Cook together, stirring occasionally, until the pasta is al dente and the greens are tender, 8β11 minutes more (taste a piece of pasta; it should be just firm in the center). Reserve 0.75 cup of the cooking water, then drain.
Combine: Return the skillet to medium heat. Add the drained pasta and greens along with 0.5 cup reserved cooking water. Toss vigorously until the oil, anchovy, and pasta water emulsify and coat the orecchiette, 1β2 minutes; add a splash more water if it looks dry. Adjust seasoning to taste.
Serve immediately, sprinkling each portion generously with the toasted breadcrumbs.