Preheat the oven to 400°F.
In a large ovenproof or regular skillet, heat the olive oil over medium heat. Add the onion and sauté for 1 minute.
Add the garlic and cook for 30 seconds, or until fragrant.
Add the beef and cook, stirring and breaking up the meat with the back of the spoon, for 5 minutes, or until no longer pink. Stir in the thyme and rosemary.
Add the green beans to the skillet, season with sea salt and black pepper to taste, and stir to combine. Cook for 5 minutes, or until the green beans soften. Stir in the cream cheese and dill.
If using an ovenproof skillet, top the mixture with the cheddar. If not, first transfer the mixture to a baking dish and then top with the cheddar. Bake for 10 minutes, or until the cheese melts. Garnish with additional dill, if desired.