Heat oil in a large skillet over medium-high heat. Season pork with salt and pepper. Place pork in the hot skillet and sear until brown on all sides, about 3 to 4 minutes per side. Transfer pork to a 6-quart slow cooker.

Add garlic cloves to the skillet. Cook, stirring often, over medium-high heat until brown, about 5 minutes. Add onion and cook until softened, about 3 minutes. Sprinkle flour over garlic and onion and cook, stirring, for 2 minutes.

Pour chicken broth into the pan and bring to a boil while scraping the browned bits of food off the bottom of the pan with a wooden spoon. Stir in lemon juice, Italian seasoning, salt, and pepper, and bring to a boil. Pour broth mixture and honey over the pork in the slow cooker.

Close the lid and cook on High for 3 hours or on Low for 6 hours, until pork is fork-tender. Transfer pork to a platter and let rest for 5 minutes. Pour cooking liquid into a saucepan and bring to a boil. Reduce heat to medium-low and simmer until thick, 2 to 3 minutes. Lightly mash the garlic cloves. Slice the pork, and serve with the mashed garlic cloves and sauce.