Preheat the oven to 350 degrees F. Generously brush six 6-to-8-ounce ramekins with butter. Combine the cheddar, parmesan, chives, flour and cayenne in a large bowl. Thinly slice the potatoes a little less than 1/8 inch thick (a mandoline works well) and add to the cheese mixture. Add 1 teaspoon salt and a pinch of black pepper and toss to combine.
Divide half of the potato-cheese mixture among the prepared ramekins, filling them about halfway (arrange the potato slices so they go to the edge of the ramekins). Top with half of the cream. Repeat with the remaining potato-cheese mixture and cream.
Transfer the ramekins to a baking sheet, cover each with foil and bake until the liquid is bubbly and the potatoes begin to soften but are not completely cooked through, about 40 minutes. Increase the oven temperature to 425 degrees F, uncover the ramekins and bake until the potatoes are tender and golden brown, 15 to 20 minutes. Run a knife around the edges and let stand 10 minutes before serving.