Pat beef chunks completely dry with paper towels, then season generously with salt and pepper on all sides.
Heat oil in a Dutch oven over medium-high heat until shimmering. Working in batches, sear beef 3–4 minutes per side until deeply golden, then transfer to a plate.
Reduce heat to medium, add onions to the same pot, and cook 5–6 minutes until softened. Add garlic and cook 1 minute, scraping up any browned bits from the bottom.
Return beef and accumulated juices to the pot. Pour in broth, add bay leaves, thyme, pepper, and celery seed. Bring to a boil, then reduce to a gentle simmer, cover slightly ajar, and cook 2 to 2.5 hours until fork-tender.
Whisk flour and salt in a large bowl, make a well in the center, and add eggs, milk, and melted butter. Gradually mix until a dough forms, then turn out and knead 8–10 minutes until smooth and elastic.
Cover the dough with a damp towel and let rest for 30 minutes to relax the gluten.
Divide dough into 4 portions, roll each to about 1/8-inch thickness on a floured surface, and cut into 1/2-inch-wide strips. Dust cut noodles with flour and let rest.
Remove bay leaves and discard. Whisk flour and cold water into a smooth slurry, then slowly stir into the simmering pot. Cook 3–4 minutes, stirring constantly, until the gravy coats the back of a spoon.
Bring gravy to a gentle boil, add fresh noodles, and cook 15–20 minutes over medium-low heat, stirring occasionally, until tender with a slight chew. Add a splash of broth if gravy becomes too thick.
Remove from heat, let stand 5 minutes, then garnish with fresh parsley if desired and serve.