Preheat the oven to 400.
Trim the ends of the leeks and discard the rough outer leaves. Slice them in half lengthwise then chop them. Put them in a colander and rinse well, then drain.
Put a large skillet on medium heat and add the butter and oil, then the garlic. Cook just a minute or so, until the garlic just barely starts to color. Add the leeks and thyme leaves and stir well. Cook about 10 minutes, until the leeks are softened. Remove from the heat.
Season the leeks with salt and pepper, then stir in the cream and half the cheese.
Put this into a casserole dish that fits the leeks about 1" deep. Sprinkle the rest of the cheese on the leeks and then bake about 20 minutes.