For the pot roast: Preheat the oven to 350 degrees F.
Sprinkle the chuck roast with 3 teaspoons kosher salt and 1 teaspoon black pepper.
Heat the vegetable oil over high heat in a rondeau or large Dutch oven until it begins to shimmer. Sear the beef on all sides to a deep brown, about 3 minutes per side; remove to a plate.
Add the onions to the pan and reduce the heat to medium. Cook until caramelized, 6 to 8 minutes. Add the carrots and celery, and cook for 5 minutes. Stir in the tomato paste; cook 1 to 2 minutes more.
Deglaze the pan with the red wine and cook until reduced by half, 6 to 8 minutes. Put the roast and any accumulated juices back in the pan. Add veal broth to cover by two-thirds. Bring to a simmer, then cover with a lid.
Transfer to the oven and cook until the roast registers an internal temperature of 190 degrees F, 1 1/2 to 2 hours. Baste every 20 minutes during cooking, and turn the beef over in the broth periodically.
Remove the roast to a cutting board and let rest for 10 minutes.
Meanwhile, skim the broth of fat and bring to a simmer on the stovetop. Melt the butter in a saute pan and stir in the flour to make a roux. Whisk the roux into the simmering broth; cook for 15 minutes.
Slice the beef against the grain. Put the slices in the sauce, and hold.
For the mashed potatoes: Place the potatoes in a tall pot; add cold water to cover. Bring to a boil over high heat and cook until the potatoes are tender, about 20 minutes.
Strain the potatoes and allow them to sit for 2 to 3 minutes to dry out a bit. Wipe the pot dry. Run the potatoes through a ricer into the pot. Add the sour cream and butter, and mix well. Season with salt and white pepper.
For the green beans and carrots: Preheat the oven to 450 degrees F. Bring 1 gallon water to a boil and season with 2 ounces kosher salt. Set up an ice bath for shocking the green beans.
Add one-third of the green beans to the boiling water; cook until al dente, 2 to 3 minutes. With a slotted spoon, transfer the beans to the ice bath to stop cooking. Dry the beans well on paper towels. Repeat two more times, until all the green beans are blanched.
In a bowl, toss the carrots with 2 tablespoons of the grapeseed oil, and season with salt and pepper. Spread the carrots on a baking sheet, transfer to the oven, and cook until tender and browned, about 15 minutes.
In a large skillet heat the remaining 2 tablespoons grapeseed oil over medium heat. Add the blanched green beans and roasted carrots, and saute for 11 to 12 minutes. Season with salt and pepper.
To plate: Divide the mashed potatoes between 6 large pasta bowls. Arrange the green beans on top of the potatoes, then arrange the beef slices on top of the beans. Ladle some of the sauce over the beef. Garnish with chopped parsley if desired. Serve immediately.