Heat 3 tablespoons olive oil in a skillet over medium heat. Add garlic; cook and stir until light brown, about 2 minutes. Transfer to a slow cooker and add chicken stock and ham hocks. Cover and cook on Low, 8 hours to overnight.

Remove 2 cups of liquid from the slow cooker and set aside. Heat 2 tablespoons olive oil in a skillet over medium heat. Add 1/4 the collard greens, 1/4 the cubed ham, and 1 teaspoon red pepper; season with salt and black pepper. Pour in 1/2 cup of the reserved liquid. Cook, stirring occasionally, until greens are bright green and slightly wilted, about 4 minutes. Transfer mixture to the slow cooker. Repeat 3 more times with the remaining greens, ham, red pepper, and slow cooker liquid.

Cook on Low until flavors meld, 4 to 6 hours.