Brown the ground beef. Heat 2 tablespoons of olive oil in a large, deep skillet or Dutch oven over medium-high heat. Add the ground beef and cook for 8–10 minutes, breaking it into small crumbles as it browns. Season with 1 teaspoon of salt and black pepper. Drain any excess grease if needed.
Cook the vegetables. Reduce the heat to medium. Add the butter, chopped onion, sliced carrots, and celery. Cook for 5–6 minutes, stirring occasionally, until the onion begins to soften. Stir in the minced garlic and cook for another 30 seconds, just until fragrant.
Add the flour. Sprinkle the flour evenly over the beef and vegetables. Stir well until everything is lightly coated, then cook for 1–2 minutes to remove the raw flour taste.
Make the gravy. Gradually pour in the beef broth, stirring well to prevent lumps and scraping up any browned bits from the bottom of the skillet. Stir in the Dijon mustard and Worcestershire sauce until combined.
Add the potatoes and seasonings. Add the diced potatoes, sweet paprika, dried thyme, and bay leaf. Stir gently to combine and bring the stew to a gentle simmer.
Simmer until tender. Reduce the heat to low, cover, and simmer for 35–40 minutes, or until the potatoes are fork-tender. Stir gently every 7 minutes, scraping the bottom of the skillet to prevent the thick gravy from sticking. Cooking time may vary depending on the potatoes.
Finish and serve. Remove the bay leaf and taste the gravy, adding a little more salt and black pepper if needed. If the gravy is too thick, stir in a splash of warm beef broth. Let the stew rest for 5 minutes, then sprinkle with freshly chopped parsley and serve warm.