Preheat the oven to 425°F. Bring a large pot of salted water to a boil.
Cut the carrots and parsnips into ¾-inch batons. Halve the potatoes and Brussels sprouts, keeping the sprouts separate.
Boil the carrots, parsnips, and potatoes for exactly 4 minutes. Drain and pat completely dry.
Toss the parboiled vegetables with 3 tablespoons olive oil, the garlic, and 1½ teaspoons kosher salt. Spread evenly across two rimmed sheet pans, spacing every piece so it isn't touching another.
Roast for 20 minutes, swapping the pans between oven racks halfway through.
Toss the Brussels sprouts with the remaining 1 tablespoon olive oil and remaining ½ teaspoon salt. Tuck into the gaps on both pans and roast another 15–18 minutes, until roots are deeply golden and sprouts are charred at the edges.
While the vegetables finish, melt the butter in a small saucepan over medium-low heat. Stir in the honey and a pinch of salt, and simmer 2–3 minutes until slightly thickened.
Transfer the roasted vegetables to a large bowl. Pour the warm glaze over them and toss gently to coat.
Stir in the fresh thyme and finish with a sprinkle of flaky sea salt just before serving.