Whisk together cider, vinegar, shallot, mustard, sugar, salt and pepper in a medium bowl, then add 3 tablespoons of the oil in a slow, steady stream, whisking to form an emulsified vinaigrette.
Rinse the broccolini, dry it thoroughly and place in a large mixing bowl. Toss it with the remaining 2 tablespoons of oil until evenly coated. Place on the grill grate and cook 4-5 minutes.
Transfer to a platter. Drizzle the cider vinaigrette on the broccoli rabe. Toss gently to coat and sprinkle on almonds. Serve warm or at room temperature.
The broccolini can be grilled 2-3 hours before serving and served at room temperature. Toss with dressing and almonds just before serving. If you don't have a grill, you can also roast this broccolini in the oven, though it won't have the same smoky flavor and bright green color. Roast it in a 400-degree oven for 10-15 minutes.