Heat up a large skillet under medium heat and add olive oil. When shimmering, add pot roast and brown on both sides, maybe 3-5 minutes per side. Place pot roast in crockpot.
In same skillet, add onions, garlic, and green pepper. Cook until translucent and soft, about 5 minutes. Sprinkle the vegetables with flour and stir continuously for 1 minute. The flour will create a subtle added starchiness and help to thicken the sauce.
Add the canned tomatoes, tomato paste, bay leaf, thyme, sugar, parsley, and red wine. Stir until tomato paste is well incorporated throughout. Season with salt and pepper to taste. Bring to a boil, then simmer for about 3-5 minutes to allow to slightly thicken.
Carefully add vegetable mixture to pot roast in crockpot. Cover and let sit at high for about 1 hour. Then turn to low and can leave for up to 8 hours. I let mine sit a working day, so about 8 hours.
About 30 minutes before you're ready to serve, add the carrots and celery. You could add these add the beginning if you wanted to, but they would be a little mushy. I like my carrots and celery to be slightly crunchy but still somewhat tender. When carrots and celery are to your liking, serve pot roast and vegetables with white rice, mashed potatoes, or just by itself!