Add ½ cup cherries to a medium saucepan along with the other dressing ingredients and bring to a boil. Lower the heat and simmer just a few minutes. Carefully transfer the mixture to a blender and blend until smooth.
Preheat the oven to 400°F. Place the broccolini on a parchment-lined baking sheet, drizzle with olive oil, and sprinkle with salt. Toss the remaining 1 cup cherries on top of the broccolini, then drizzle with the dressing, reserving some for serving, if desired. Roast in the oven for 20-25 minutes. Serve immediately.