Bring a large pot of salted water to boil and add bucatini. Bucatini takes a couple minutes longer than traditional spaghetti. When pasta is almost al dente, add broccolini to the boiling water. When the pasta and broccolini are ready, drain and add them back into the hot pot. You want the broccolini to remain bright green and still have a bite to it.
While the pasta and broccolini are cooking, heat a medium cast iron skillet and oil over medium-high heat.
Salt and pepper both sides of the scallops and sear in the hot oil, 2-3 minutes per side. The scallops will loosen from the pan when they're perfectly golden, so don't force them.
To make the sage browned butter, heat a medium pan over medium heat and allow butter to melt with the sage leaves. Swirl occasionally as it starts to brown, being careful not to burn it. The butter will smell sweet and nutty when it's ready.
Pour browned butter over bucatini and broccolini and toss to coat. Toss with grated parmesan and season with salt and pepper, to taste.
Serve pasta with seared scallops on top and addition sage and parmesan, if desired.