Cut bagette into slices, about ¾-inch thick.
Heat 10-inch cast iron frying pan on lowest heat.
Add about ¼ inch olive oil and garlic cloves.
Cook on lowest heat, stirring frequently, until garlic cloves are golden and soft. This could take 15 minutes or more.
Remove garlic cloves from the pan and set them aside to use later.
Drain most of the garlic oil from the pan and set that aside as well. Leave enough oil in the pan to coat the bottom liberally.
Increase heat to medium-low. Place bagette slices in pan in a single layer. Spoon additional garlic oil on top of slices, ½ or so teaspoons per slice.
Fry until slices begin turning golden brown. The amount of time will vary, so watch the slices closely. Turn and repeat.
Remove cooked slices to a plate. Cook additional slices as needed.