Heat the oven to 350°F. Grease an 8 by 4-inch loaf pan with cooking spray or softened butter, or brush with olive oil. Line the bottom with a long sheet of parchment that extends up the two short ends of the pan.
Rub the thyme into the sugar with your fingers in a large bowl. Whisk in the oil and then the eggs, one at a time. Whisk in the buttermilk, and then the baking powder, salt, and pepper. Gently fold in the flour until you still see a few streaks and then fold in the cheese and tomatoes, until the last of the flour disappears.
Transfer the batter to the prepared pan and bake for 25 to 30 minutes until a wooden skewer inserted in the center comes out with a moist crumb or two. Let cool until you can easily lift the bread out of the pan by its parchment handles, running a knife around the edges if it resists. Serve warm or at room temp with salted butter.