First, melt the butter in a small saucepan over medium heat. Once it's melted, remove it from the heat and whisk in the maple syrup, grainy mustard, Dijon mustard, lemon juice, salt, and pepper. Continue whisking until the mixture is smooth and all the ingredients are well combined.
Next, preheat your oven to 400°F (200°C). While the oven heats up, wash, peel, and trim the green tops off your carrots. Place them on a large baking sheet and pour most of the glaze over them, saving a tablespoon or two for later. Toss the carrots gently to ensure they are all evenly coated.
Spread the glazed carrots in a single layer on the baking sheet. This ensures they roast evenly instead of steaming. Place the sheet in the preheated oven and roast for 30-35 minutes. Stir them once halfway through to prevent the glaze from burning and to promote even caramelization. The carrots are done when they are tender enough to be pierced with a fork.
Once the carrots are tender and beautifully glazed, remove them from the oven. Transfer them to a serving platter and drizzle the remaining glaze over the top for an extra shine and burst of flavor. It's best to serve them immediately while they are warm and the glaze is at its most luscious.