Wash the produce
Rinse the Onion (sliced), Carrots (sliced), Garlic (minced), Thyme (fresh), and Rosemary (fresh) under cool water as needed, then pat everything dry. Clean, dry vegetables will brown better in the pan instead of steaming.
Cut the vegetables
Slice the onion into thin half-moons, slice the carrots into coins or half-moons about the same thickness so they cook evenly, and mince the garlic finely. Pick the thyme leaves from the stems if the stems are tough, and strip the rosemary leaves from the woody stem, then give the rosemary a rough chop.
Dredge the beef
Pat the Beef Chuck (or similar stewing beef) very dry with paper towels, then place it in a bowl or on a tray and toss it with the All-Purpose Flour (for dredging) until each piece is lightly coated. You want a thin dusting, not a heavy batter-like layer.
Heat the pan
Set a large heavy pot or skillet over medium-high heat and add the Olive Oil. Let the oil heat until it looks fluid and shimmery and the pan feels properly hot, which should take 1 to 2 minutes.
Brown the beef
Add the floured beef to the hot pan in batches, leaving space between the pieces. Sear until deeply browned on one side, then turn and brown the remaining sides. Transfer each batch to the slow cooker as it finishes. Keep the heat lively so you build good color, but avoid crowding the pan.
Soften the vegetables
In the same pot, add the sliced onion and carrots to the flavorful drippings left behind from the beef. Cook, stirring often, for 4 to 5 minutes, until the onion starts to soften and turn lightly golden and the carrots begin to lose their raw edge.
Add garlic and herbs
Stir in the minced garlic, the thyme, the rosemary, and the Bay Leaf. Cook for about 30 seconds, just until fragrant, stirring constantly so the garlic does not scorch.
Deglaze the pot
Pour in a splash of the Beef Broth (or stock) and scrape the bottom of the pot with a wooden spoon to lift all the browned bits. Let everything bubble briefly so those flavorful bits dissolve into the liquid.
Fill the slow cooker
Transfer the vegetable mixture into the slow cooker with the browned beef. Pour in more beef broth until the ingredients are mostly covered but not completely submerged. Cover with the lid.
Cook until tender
Cook on low for 7 to 8 hours or on high for 4 to 5 hours, until the beef is very tender and pulls apart easily with a fork. The finished beef should shred with very little resistance.
Shred the beef
Lift the beef out of the slow cooker and shred it with two forks, discarding any large pieces of fat. Remove and discard the bay leaf as well.
Return and serve
Return the shredded beef to the cooking liquid and stir well so every strand is coated. Serve hot, spooning plenty of the savory juices over the top, especially if you're serving it over mashed potatoes.
