Blanche Broccolini® in large saucepan of boiling salted water until crisp-tender, 2 minutes and drain. Transfer to bowl of ice water to cool. Drain, pat dry with paper towels.
Cook Butternut Squash in large pot of boiling water until just tender, about 6 minutes. Drain; Rinse with cold water and transfer to large bowl. Sprinkle vermouth over warm butternut squash; toss gently and let stand 5 minutes. Whisk vinegar, shallot, and mustard in small bowl. Gradually whisk in oil. Pour over butternut squash and toss to coat. Cool completely. Mix in Broccolini® and parsley. Season to taste with salt and pepper. (Can be made 1 day ahead) Cover and refrigerate. Serve cold or at room temperature.