Preheat oven to 400ºF.
Heat 1 Tbsp of olive oil in a cast iron skillet (or heavy-bottom, oven-safe pan) over medium-high heat. Add the shallots to the pan, and quickly caramelize; stirring for 1-2 minutes. Once the shallots are caramelized, add another Tbsp of olive oil and the butter to the pan; then add the Brussels sprouts, turnips, salt and pepper.
Continue to cook, stirring occasionally for another 8-10 minutes, or until the vegetables begin to caramelize.
Meanwhile, whisk together the Dijon mustard, maple syrup, 1 Tbsp of olive oil, the juice from half a lemon, and the red pepper flakes.
Once your vegetables have some color, stir the dressing into the vegetables and place the cast iron skillet in the oven. Roast for 25-30 minutes, or until the turnips and Brussels sprouts are tender.
Remove from the oven. Add additional salt, pepper and/or maple syrup if necessary.