In a large skillet, over medium high heat, add the butter and melt. Season chicken with salt and pepper, and place in the skillet with the melted butter. Cook each side for 1-2 minutes or until they have a nice sear and are nicely brown.
Add potatoes, carrots, green beans, garlic, Parmesan, parsley, thyme, and oregano to your slow cooker. Stir to mix well. Season with salt and pepper, drizzle with olive oil, and mix again to coat.
Top the vegetables with the browned chicken and cover. Cook on low for 6 hours or high for 4, or until veggies are tender. Serve veggies and chicken topped with more Parmesan, if desired.