Combine the olive oil, bay leaves, peppercorns, and thyme in a small heavy saucepan. Set over moderate heat and cook, stirring occasionally, until the oil is very hot, about 5 minutes.
Arrange the cheeses in a single layer in a small heatproof bowl or pan. Sprinkle the chopped basil and garlic over the cheeses and then pour the hot oil and seasonings over them.