General Motors Co. dealers across the U.S. on Monday will begin repairing faulty ignition switches in Chevrolet Cobalts and other models, a big hurdle in getting past the company’s mishandling of its recall.

More than 2.3 million car owners are expected to roll into service bays over the next six months for a repair that takes roughly 30 minutes to 45 minutes to complete.

“Customers will be receiving letters this week to…