Prep the Veggies: Preheat your oven to 375°F / 190°C. Lightly butter a medium shallow baking dish.
Using a sharp vegetable peeler, peel the rutabaga and carrot.
Grate them using the large holes of a box grater or the shredding disk of a food processor.
Sauté the Base: In a large skillet, melt 2 tablespoons (30 ml / 1 fl oz) of the butter over medium-high heat.
Add the grated rutabaga and carrot and sauté for 10 minutes, stirring frequently. The goal is to soften the vegetables, not to brown them.
Assemble the Gratin: Transfer the sautéed vegetable mixture to your prepared baking dish and spread it into an even layer.
Season generously with salt and freshly ground black pepper.
Pour the heavy cream evenly over the top, ensuring as much of the mixture is coated as possible.
Add Topping and Bake: Sprinkle the bread crumbs evenly over the cream-soaked vegetables.
Cut the remaining 1 tablespoon (15 ml / 0.5 fl oz) of butter into small pieces and dot them over the top.
Bake for 20 to 25 minutes, or until the cream is bubbling and thickened and the topping is golden brown and crisp.
Let rest for a few minutes before serving hot.