Season roast liberally with salt and pepper. Heat 2 teaspoons oil in 12-inch skillet over medium-high heat until shimmering but not smoking. Brown roast thoroughly on all sides, 8 to 10 minutes. Transfer browned roast to slow-cooker insert.
Reduce heat to medium. Add remaining 2 teaspoons oil to empty skillet, along with onions, celery, carrots, and garlic. Cook, stirring occasionally, until lightly browned, about 4 minutes. Transfer to slow-cooker insert.
Increase heat to high. Add red wine to empty skillet, scraping up any browned bits with wooden spoon, and simmer for 5 minutes. Add tomatoes and broth and bring to boil. Add pepper flakes, bay leaves, and thyme and transfer to slow-cooker insert.
Set slow cooker to high, cover, and cook until tender, 6 to 7 hours. (Alternatively, cook on low for 9 to 10 hours.) Transfer roast to carving board; loosely tent with foil to keep warm. Discard bay leaves. Allow liquid in pot to settle, about 5 minutes, then use wide spoon to skim fat off surface. Puree liquid and solids in batches in blender or food processor. (Alternatively, use immersion blender and process until smooth.) Stir in parsley and season to taste with salt and pepper.
Remove strings from roast and cut into 1/2-inch-thick slices. Transfer meat to warmed serving platter. Pour about 1 cup gravy over meat. Serve, passing more gravy separately.