Lightly season the roast all over with salt and pepper. On a large platter, mix together 3 tbsp of the flour, 1 tsp salt, and 1/2 tsp of pepper. Turn the roast in the seasoned flour, shaking off any excess.
In a large Dutch oven, or large saucepan, heat the oil and butter over medium heat.
Add the roast and cook, turning occasionally, until browned on all sides, about 10 minutes. Remove from the pan and set aside. Pour off all but 2 tbsp of the oil in the pan.
Add the finely chopped carrots, yellow onion, and celery and saute over medium-high heat until softened, about 5 minutes.
Stir in the remaining 2 tbsp of flour and cook for about 1 minute.
Pour in the beef stock and deglaze the pan, stirring and scraping up the browned bits on the bottom of the pan. Bring to a simmer.
FOR SLOW COOKING THE OVEN
Preheat the oven to 325°F.
Nestle the roast into the vegetables and cooked stock. Cover and place in the oven for 2½ hours.
Remove from the oven, uncover and stir in the potatoes, large carrot pieces, and pearl onions. Cover and return to the oven for another 30 minutes. Stir in the peas and place in the oven for another 20 minutes, or until the vegetables are tender.
FOR USING YOUR SLOW-COOKER
Transfer the roast to your slow cooker.
Pour the vegetable and stock mixture over the meat and cook for 4 hours on high or 8 hours on low.
Uncover and stir in the potatoes, carrot pieces, and pearl onions.
Cover and cook for 45 minutes.
Uncover and stir in the peas.
Cover and cook until all the veggies are tender, about 15 minutes longer.
FINISHING THE ROAST
Transfer the roast to a cutting board and cover with aluminum foil to keep warm.
Use a slotted spoon to remove the potatoes, large carrot pieces, onions and peas. Place in a large bowl and cover with foil to keep warm.
Strain the cooking liquid through a fine-mesh sieve, or a colander with cheese cloth, discarding the excess solids.
Bring the strained liquid to a boil over high heat and cook until the liquid is slightly thickened, about 10 minutes. Taste and add more salt, if desired.
Slice the roast against the grain and place the slices on a serving dish and then arrange the roasted veggies around the meat. Drizzle the sauce over the meat and veggies. Serve at once, passing extra gravy on the table.
If using a Dutch oven, you can prepare everything in the pot. If using a roasting pan, you'll need to saute the roast and then the vegetable in a large saucepan and then pour over the seared roast in a small roasting pan. Be sure to cover when braising the roast in the oven. You'd also need to use a large saucepan if preparing the roast in a slow cooker.The meat and vegetables can be prepared up to 12 hours in advance. Keep covered in the refrigerator and then place in the Dutch oven/roasting pan or slow cooker when ready to finish cooking the roast. All the meat to come to room temperature before cooking. Left over will keep in the refrigerator for up to 1 week and freezes beautifully for up to 2 months.Next day roast beef sandwich (with the gravy) is amazing!