Arrange a rack 6 inches from the broiler heat source and another rack in the center of the oven. Heat the oven to 425 degrees.

Line a sheet pan with parchment paper or foil. Prick the sweet potatoes all over with a fork and place on the pan. Bake on the center rack until the potatoes are fork-tender, 1 to 1 ½ hours.

Meanwhile, in a small saucepan, heat the heavy cream, bay leaves and black pepper until bubbling at the edges and steaming. Remove from the heat and let steep until the cream is fragrant and the potatoes are cool enough to handle.

Using your fingers, peel the potatoes (the skins should slip right off), then add the flesh to a large bowl. Pour the cream over the potatoes, holding back the bay leaves and discarding them, then add the butter, brown sugar and salt. Whisk until smooth. Taste and add more salt and pepper if desired (the potatoes should taste deeply savory, like mashed potatoes). Set aside to cool slightly.

Reduce the oven temperature to 350 degrees. Grease a 2-quart shallow casserole dish with butter. Whisk the eggs into the potatoes until fluffy, about a minute. Spread the mixture in the dish, then place the marshmallow halves, cut sides down, in a single layer across the top, leaving small slivers of space between them (they’ll expand as they bake). Sprinkle with the pecans. (You can cover and refrigerate the casserole at this point for up to 2 days, until ready to bake.)

Bake until lightly browned on top and hot through the center, 20 to 25 minutes. (If the casserole was refrigerated, it may take longer to heat through.) Take the casserole out of the oven and heat the broiler.

Place the dish under the broiler until you see a wisp of smoke and the marshmallows are deeply and evenly browned, 1 to 2 minutes. Do not take your eyes off the dish, as the marshmallows can burn in an instant. Serve hot or warm.