Bring a large pot of well-salted water to a boil. Drop in the baby potatoes and simmer until tender, about 15 minutes. Remove and set aside. Cut in half when cool enough to handle. Keep the water simmering.
Trim the bottoms of the broccoli rabe stalks and chop into 2-inch lengths. Drop the rabe into the water you used to cook the potatoes, and simmer for 10 – 15 minutes, or until just tender. Drain in a colander and spray with cold water. Press the rabe into the colander to try to remove as much water as possible. Finish by rolling the rabe up in a towel and squeezing out the last bit of water. Set aside.
In a medium sauté pan, over medium heat, sauté the onion until soft and golden. Add the halved potatoes. Sauté for 1 minute, just to reheat them. Add the rabe and toss in the pan to mix well. Add the lemon juice, sweet paprika, salt and vinegar.
Heat the butter in a small pan over low heat. Add the anchovies and a pinch of crushed red peppers. Sauté for a couple of minutes, stirring as the anchovies melt into the butter. Add the garlic and red pepper flakes and sauté for another minute. Add half of the browned butter bread crumbs.
Add the anchovy mixture to the rabe and toss to coat. Correct for seasoning and top with remaining browned butter breadcrumbs when served.