Cut off and discard the lower part of the broccoli rabe stems, leaving the broccoli about 8 inches long. Remove the large tough leaves, leaving just tender leaves and flower buds. Peel the thick, lower part of the stems by lifting strips from the stem end with a paring knife or vegetable peeler and drawing them up toward the bud area. A perfect peel is not necessary, but removing the peel does remove bitterness. Cut the stems into 1 1/2 to 2-inch lengths. Wash the broccoli thoroughly and dry it well, preferably in a salad spinner. Remove the casing from the sausage and crumble it. In a large skillet heat the olive oil over medium-high heat. Add the sausage meat and cook until the sausage is no longer pink, about 3 minutes. Add the crushed garlic and continue sautéing until the sausage is lightly browned, about 2 to 3 minutes. Meanwhile, bring 6 quarts of salted water to a boil. Drain the fat from the pan and add the remaining 4 tablespoons of olive oil. Add about half the broccoli rabe to the pan and toss it until it begins to wilt. Add more of the broccoli as that in the pan begins to wilt. When all the broccoli rabe has been added, cover the pan and steam the broccoli until wilted and bright green, about 4 minutes. Taste and season lightly with salt and red pepper flakes. Stir in the butter until melted, then add the stock and bring to a boil. Boil gently, uncovered, for several minutes more to reduce and concentrate the liquid. Again taste and correct the seasoning. Set the broccoli aside until the pasta is ready. Cook the orecchiette. Drain them well and return them to the pan over low heat. Add the broccoli rabe sauce and toss gently to blend. Taste carefully for seasoning, and remove from heat. Add half of the grated cheese and toss to blend. Transfer to a serving platter or individual bowls and sprinkle with the rest of the grated cheese. Serve immediately.