Heat olive oil in a large oven-safe skillet over medium-high heat. Add ground beef and cook until browned, breaking it up with a spoon. Add onions, carrots, and celery, cooking until vegetables begin to soften (about 5 minutes). Stir in garlic and cook for 1 minute until fragrant.

Sprinkle flour over the beef mixture and stir constantly for 1 minute. Gradually pour in beef broth while stirring to prevent lumps. Add Worcestershire sauce, thyme, paprika, salt, and pepper. Bring to a simmer and cook until thickened (about 3-4 minutes). Stir in frozen peas, then remove from heat.

In a medium bowl, whisk together flour, baking powder, and salt. Cut in cold butter using a pastry cutter or your fingers until mixture resembles coarse crumbs. Stir in fresh parsley, rosemary, and oregano. Gradually add milk, stirring just until dough comes together (do not overmix).

Drop spoonfuls of biscuit dough evenly over the beef filling in the skillet. Transfer skillet to a preheated 400°F (200°C) oven and bake for 18-22 minutes, until biscuits are golden brown and filling is bubbly. Let rest for 5 minutes before serving.