Melt the butter over medium heat in a small saucepan, stirring often, until melted. It will start to bubble, foam, and separate then will turn golden brown with a nutty aroma. Side Note: Watch the butter carefully while cooking because it can burn quickly & easily.
Remove from the heat and immediately add the vinegar and stir; add the maple syrup and stir until well combined. Side Note: Be careful because it will pop and splatter a bit.
Arrange the carrots on the prepared baking sheet in an even layer.
Drizzle half of the browned butter sauce over the heirloom carrots then season with sea salt and freshly cracked pepper, to taste, then toss to coat evenly. Reserve the remaining sauce for serving.
Bake until the carrots are caramelized and fork-tender, about 20-25 minutes, flipping them halfway through roasting.
Transfer the carrots to a serving platter.
Reheat the reserved sauce until warm then drizzle it over the heirloom carrots. Sprinkle with chopped parsley.