Bring a large pot of salted water to a boil. Chop the broccolini into florets, keeping the stems long.
When the water is boiling, add the broccolini and cook it for 2 minutes. Remove it from the water with tongs and place it in an ice bath for a minute or so until cool. Pat the florets dry.
Meanwhile, thinly slice the red onion into slivers (you may want to rinse or let it soak in water ot remove some of the bite, then shake it dry). Thinly slice the mushrooms.
In a medium bowl, whisk the white wine vinegar, Dijon mustard, maple syrup or sugar, and kosher salt. Gradually whisk in the olive oil 1 tablespoon at a time.
In a large bowl, mix together the broccolini, red onion, raw mushrooms, dill sprigs, Parmesan shavings, and vinaigrette dressing. If desired, garnish with lemon zest. Serve immediately. The flavor is best fresh, but you can store leftovers refrigerated. (You may need to add a bit of salt or a splash of white wine vinegar to revive the flavors after refrigerating.)