Heat 1 tablespoon of olive oil or avocado oil in a large Dutch oven or heavy pot over medium-high heat. Pat the beef cubes dry with paper towels, season with salt and black pepper, and brown them in batches, about 3-4 minutes per side. Remove the beef and set aside.
Return the browned beef to the pot. Add the carrots, parsnips, sweet potato, beef broth, diced tomatoes, thyme, and rosemary. Stir to combine, ensuring the beef and vegetables are mostly submerged in the liquid.
Bring the mixture to a boil, then reduce the heat to low. Cover and simmer for 1.5 to 2 hours, stirring occasionally, until the beef is tender and the vegetables are cooked through. If the stew thickens too much, add a splash of extra broth or water.
Taste and adjust seasoning with additional salt and pepper as needed. Remove from heat and let the stew rest for 5-10 minutes to allow the flavors to meld.
Ladle the stew into bowls and garnish with fresh parsley if desired. Serve your Paleo beef stew hot and enjoy a warm, hearty meal!