Bring a large pot of water to a boil over high heat. Season well with salt. Add the broccoli rabe to the water and simmer until the stem is just tender when pierced with a knife, 2 to 3 minutes. Remove to a rimmed baking sheet to cool slightly. When cool enough to handle, squeeze out any extra water with a clean kitchen towel or paper towels.
Add the almonds to a food processor and pulse until finely chopped, 5 or 6 times. Add the basil, oil and 1/2 teaspoon salt. Puree until combined and almost smooth. Pour the pesto into a large bowl. Add the Parmigiano-Reggiano, broccoli rabe and mozzarella and toss well to combine.
Bring a large pot of water to a boil. Season liberally with salt. Add the orecchiette and cook until al dente, about 8 minutes. Using a slotted spoon or a pasta spider, transfer the pasta directly to the bowl with the pesto. Add 1/2 cup of the pasta water and 1/2 teaspoon salt and toss everything together until evenly coated.