In a large skillet, cook the butter, onions, and garlic over medium heat, stirring occasionally. Cook until the onions are translucent and the butter is lightly browning. Whisk in the flour, salt, black pepper, thyme, broth, and half-and-half. Cook and whisk until no flour lumps remain, then simmer over medium-low heat until thick. I simmer mine for 10 minutes. You want it to be a very thick gravy; simmer longer if necessary. Taste and add more seasonings if you prefer. Sometimes I add more thyme. Remove from heat and set aside.