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Step 1
For the broccoli: Preheat the oven to 375 degrees F. Line 2 baking sheets with parchment paper.
Step 2
Cut the florets into small, fairly even-sized pieces. Trim off the hard bottom of the stems and peel the stems like carrots. Cut the peeled stems into about 1/2-inch rounds. You should have 8 to 9 cups loosely packed broccoli. Arrange the stems and florets in a single layer on the baking sheets, with all of the stems on one sheet. Toss with the olive oil and season with salt and pepper. Roast until the broccoli florets and stems are tender and a little browned, 15 to 20 minutes.
Step 3
For the vinaigrette: In a large bowl, whisk together the mustard, oil, horseradish, lemon zest and juice and a pinch of sugar or honey. If the dressing is too thick, whisk in a splash of water. Add the tarragon.
Step 4
To serve: Toss the broccoli stems in the dressing to coat them fully. Add another pinch of sugar. Add the florets and gently toss to coat. Use scissors to cut the arugula into bite-size pieces into the bowl, add another drizzle of oil and gently toss again.