spray an 8×8-inch baking pan with nonstick spray and preheat the oven to 375 degrees F.
pour about ΒΌ cup of the cream into the bottom of the dish. next, put down a layer of potato slices (slightly overlapping), then about 2 tablespoons of chopped basil. top the basil with about 2 tablespoons of the grated cheese, and sprinkle a bit of salt and pepper over everything. repeat this layering process–cream, potatoes, basil, cheese, salt, and pepper–at least two more times, until you have used up all of the potatoes. you should be left with at least a couple tablespoons of cheese, which you should save for broiling later.
put the baking dish into the oven and bake it for 35-40 minutes, until the potatoes are completely cooked through and the top is golden. put the rest of your cheese over the top, then put the dish under the broiler for another 5 minutes, until the cheese is bubbly and brown.
serve immediately with more fresh basil over the top.