Bring a large pot of well-salted water to a boil. When the salt dissolves the water should almost taste like seawater.
Fill a large bowl 3/4 with ice and water.
Blanch each type of vegetable separately in the boiling water until they’re easy to chew, but still snappyAl dente, if you will.. Pull a piece out every few seconds to check for doneness. The broccoli should only take about 45 seconds, but the cauliflower might take more than a minute. Do the carrots next to last as they’ll discolor the water. Finish with the beets. Do not blanch the onion.
As each vegetable is ready, scoop using a wire spider strainer and deliver to the ice water bath to halt the cooking process. If you skip this step, the vegetables will continue to cook from residual heat and the final dish will be too soft.
Once cool, thoroughly drain the veggies on paper towels or cooling racks so that they are dry as possible. Meanwhile, transfer the broccoli and the onion to an airtight plastic container or zip-top bags and refrigerate.
Whisk the the tangerine, lemon, and lime juices together in a large mixing bowl along with the vinegar, garlic, shallot, mustard and 1/2 teaspoon of the kosher salt.
Whisk continuously while pouring the oil in a thin stream to emulsify. Once all the oil is worked in and the mixture has thickened, add the tarragon then the vegetables (excluding the broccoli and onion). Toss to thoroughly coat. Cover tightly and refrigerate for several hours or overnight, turning the container periodically to allow the veggies to evenly marinate.
When ready to serve, add the broccoli and onions to the bowl and toss yet again. If you add them earlier, the onions will "bleed" pink on all the vegetables and the broccoli will turn gray from the acidity.