In a medium pot, bring a few inches of water to boil for the rabe. Bring a large pot of water to boil for the pasta. Salt the water in both pots once it comes to a boil.
In the medium pot, cook the rabe until wilted, 1 to 3 minutes. Drain and transfer to a bowl of ice water to cool. Drain; chop into bite-size pieces.
In a large, deep skillet, heat the olive oil, four turns of the pan, over medium. Add the anchovies, chile and garlic. Partially cover and cook until the anchovies melt into the oil, about 1 minute. Add the rabe; season with salt and pepper. Add the vermouth and stir until evaporated, 3 to 4 minutes. Reduce the heat to low.
Add the pasta to the large pot of boiling salted water; cook until al dente. Drain the pasta, reserving half a mug of cooking water. Add the cooking water to the rabe mixture; toss with the pasta. Divide among bowls and top with ricotta salata.