Preheat the oven to 450 F. In a medium bowl, combine the sunchokes, carrots, parsnips, 3 Tbsp olive oil, the salt, and the pepper. Transfer the vegetables to a rimmed baking sheet and roast in the oven for 20 minutes, until lightly caramelized and tender, stirring once midway through cooking.
While the vegetables are roasting, place the bacon in a small sautee pan over medium-high heat and cook for 2 minutes. Add the shallots, reduce the heat to low, and cook for 5 more minutes, or until the bacon fat is rendered and the shallots are lightly caramelized. Drain, discarding all but 1 tablespoon of the fat from the pan.
Transfer the bacon/shallot mixture to a medium mixing bowl. Add the garlic, parsley, and sugar, and whisk to combine. Whisk in the vinegar. Slowly whisk in the remaining olive oil, and set aside. Transfer the roasted vegetables to the mixing bowl, and toss with the vinaigrette to combine. Serve warm.