Bring a large pot of cold water to a rolling boil. Season with plenty of salt and add the dried pasta. Cook until al dente, according to the box directions. Reserve about 3/4 cup of the pasta cooking water and then drain.
In a large skillet, combine the cheeses, black pepper, and enough cold water to make a very thick paste. Add the pasta, olive oil, and half of the reserved cooking liquid to the pot. Cook over very low heat, tossing the pasta around, until the cheese has melted and the sauce has thickened, about 5 to 7 minutes. Add as much of the remaining cooking liquid as needed to create a thick sauce, coating all of the spaghetti.
To make the broccoli rabe, bring a medium saucepan of water to a boil. Add the broccoli rabe and cook until bright green, about 5 minutes. Blanche in ice cold water and drain.
Set a large skillet over medium-high heat with the olive oil, garlic and crushed pepper flakes. Cook for about a minute to toast the garlic, and then add the broccoli rabe. Sauté, stirring often, until the broccoli has charred, about 5 minutes. Season with salt and black pepper. Add the lemon juice right at the end, before serving.
Serve the cacio e pepe with grated cheese on top and black pepper for garnish, with the broccoli rabe on the side. Enjoy!