Preheat oven to 350. Combine bread and milk in a medium bowl, pressing on bread to submerge. Let sit 10 minutes.
Place ground beef, breadcrumbs, eggs, onion, parsley, salt, pepper, and thyme in a bowl. Using your hands, mix together until well combined.
In a pan on medium-high heat, sear meatballs on both sides and remove from pan.
Melt butter and oil in a large skillet over medium-high heat. Add flour to thicken. Whisk together tomato paste and wine. Add to skillet and bring to a boil. Continue boiling 5 minutes, until liquid thickens slightly. Stir often.
Add broth, reduce heat to medium and simmer until it thickens, about 15 minutes. Season with salt and pepper. Add meatballs to finish cooking.
