Wash, dry, and peel carrots and place in a shallow dish long and wide enough to fit them all.
Add butter and thyme to a small saucepan and heat over a medium flame to melt butter. Continue to warm the butter for 1 to 2 minutes. The butter should take on a green-ish tint from the thyme leaves. Remove from heat and cool for a few minutes. In a small bowl combine maple syrup, mustards, nutmeg, and salt and pepper. Whisk in butter until smooth and well combined.
Pour the butter/syrup mixture over the carrots and toss to coat. Arrange the carrots on a parchment lined baking sheet, and use a spatula to scrape any remaining butter/syrup mixture over them. You may want to use two sheets of parchment to make sure the whole pan is completely covered.
Roast until tender and brown, for about 45 minutes to 1 hour, using tongs to turn each carrot about 30 minutes in. Watch carefully that the sugar in the maple syrup doesn’t burn onto the parchment.