Preheat your oven to 400°F (200°C). Lightly grease a medium casserole dish with butter or cooking oil.
Peel and cut the carrots into thick sticks. Wash the yellow potatoes and cut them into 1-inch pieces.
Place the prepared carrots and potatoes in the casserole dish, spreading them into an even layer.
Mix the kosher salt into the melted butter, then drizzle the mixture evenly over the vegetables.
Toss the carrots and potatoes gently to ensure all the pieces are coated with the seasoned butter.
Cover the casserole dish tightly with aluminum foil and bake for 25–30 minutes, until the vegetables begin to soften.
Carefully remove the foil, watching out for hot steam. Toss the vegetables so the pieces on top and bottom are evenly redistributed.
Return the dish to the oven and bake uncovered for another 25–35 minutes, until the vegetables are tender, golden brown, and caramelized around the edges.
Remove from the oven and spoon the buttery juices from the bottom of the dish over the vegetables before serving.
