Pat beef stew meat dry with paper towels and place on a rimmed baking sheet. Drizzle with olive oil and season with steak rub. Toss to coat well.
Grill stew meat on a hot grill with hickory chunks for smoke flavor. We are using lump charcoal on our Big Green Egg. The same method works for any charcoal grill or gas grill.
Cook with the grill closed for 30- 45 minutes or until stew meat reaches about 165°. It will continue to cook in the stew.
Remove from grill and cool slightly.
Make the Roux: Add bacon grease, vegetable oil and all purpose flour into a dutch oven or large soup pan. Cook over low heat, stirring occasionally until roux reaches desired color – between dark peanut butter and chocolate brown. The darker the roux, the more nutty and rich the flavor.
Cook the Vegetables: Peel and dice the potatoes. Dice onions and carrots. Cook carrots and onions in a large skillet in vegetable oil over medium-high heat. Stir occasionally until vegetables are softened.
Place the stew meat on a cutting board and slice into bite-size pieces.
Pour water into the dutch oven with the roux. Add the diced potatoes and the diced tomatoes with juice.
Stir in the sautéed vegetables and the sliced stew meat.
Season with Worcestershire sauce, vinegar, garlic, salt and pepper.
Cook over medium-high heat until mixture comes to a low boil, stirring often.
Lower to simmer, cook 15- 20 minutes until potatoes are softened and stew is thickened.
Ladle into bread bowls or soup bowls and serve immediately.