In a large bowl add the baking mix, the milk and the egg and whisk to combine. Stir in the ham, cheese, onion, and thyme, and season with salt and pepper, to taste.
In a high sided skillet over medium-high heat, add the oil and heat it to 365 degrees F.
In a shallow baking dish or pie plate spread out the bread crumbs and season with salt and pepper, to taste. Using a small cookie scoop or tablespoon measure, scoop out rounds of dough and drop them into the bread crumbs. Roll the dough around to coat them completely. Drop the croquettes, 5 or 6 at a time, into the hot oil and fry until deep golden brown, about 3 minutes. Remove from the oil and drain on brown paper or paper towels. Arrange them on a serving platter and serve warm.