You can substitute broccoli or broccoli rabe for broccolini if you desire (though we love the broccolini). Just be sure to halve broccoli stems and florets for faster cooking. Have fun with this one. We do, regularly.
Meanwhile, heat a medium skillet over medium-high heat. Add the olive oil and sausage to the pan, and cook, breaking up the sausage with a wooden spoon as you go, until the sausage is almost fully cooked, 6 to 8 minutes. Add the broccolini, season with ½ teaspoon salt and ¼ teaspoon pepper, and cook for about 6 minutes, stirring regularly.