Preheat the oven to 375° and butter a shallow 2-quart ceramic baking dish. In a medium saucepan, bring the heavy cream to a simmer. Whisk in the garlic and mustard and season with salt and pepper. Keep warm.
Using a mandoline, slice the turnips crosswise 1/8 inch thick. Arrange half of the turnip slices in the prepared baking dish, overlapping them slightly. Pour half of the cream mixture over the turnips and sprinkle 1/4 cup of the grated cheese on top. Repeat with the remaining turnip slices and cream. Cover tightly with foil and bake for about 1 hour and 15 minutes, until the turnips are tender.
Meanwhile, in a food processor, pulse the porcini until they resemble coarse crumbs. Add the panko and pulse 4 times. Transfer the crumbs to a small bowl and whisk in the remaining 1/4 cup of grated cheese.
Remove the casserole from the oven and uncover. Sprinkle the porcini crumbs evenly over the top and bake for about 20 minutes, until the cream is bubbling and the top is golden brown. Let stand for 15 minutes before serving.