Combine beef, 5 tablespoons Boursin cheese, ¾ teaspoon salt, and ¼ teaspoon pepper in medium bowl and knead gently until combined. Form mixture into 1-inch meatballs. Heat oil in a large nonstick skillet over medium-high heat until just smoking. Cook meatballs until well browned all over, about 5 minutes. Transfer meatballs to plate and pour off all but 1 tablespoon fat from pan.

Cook onion in reserved fat until browned, 6 to 8 minutes. Stir in flour and cook until golden, about 1 minute. Add broth, noodles, and wine and bring to boil. Cover and reduce heat to medium-low. Cook, stirring often until pasta begins to soften, about 5 minutes. Add meatballs and simmer, covered, until meatballs are cooked through and noodles are al dente, about 4 minutes. Off heat, stir in remaining Boursin cheese and chives. Season with salt and pepper to taste.