The night before, season the chuck roast liberally with salt and pepper and refrigerate uncovered.
When ready to cook, preheat the oven to 300 degrees F.
In a large Dutch oven, heat the canola oil over medium-high heat. Season the chuck roast again with salt and pepper and dust with flour, shaking off the excess. Sear on all sides, browning the meat evenly, 4 to 6 minutes per side. Remove the roast to a plate, then add the carrots, turnips and onion to the pot. Lower the heat to medium and cook, stirring occasionally, until the vegetables are caramelized, 6 to 8 minutes. Stir in the tomato paste, garlic, thyme and bay leaves and cook another 2 minutes.
Add the roast back to the pot, then add the beer and beef stock. Nestle the roast down among the vegetables so that it is mostly submerged in the liquid. Bring to a simmer. Cover, leaving the lid slightly ajar, and place in the oven to cook under very tender, 3 to 3 1/2 hours, testing with a small knife for tenderness after 3 hours.
Meanwhile, heat the butter in saucepot over medium-low heat, add the pearl onions and peas and season with salt and pepper. Cook, stirring occasionally, until the onions and peas are warmed through, 3 to 5 minutes.
Once the roast is done, remove it from the pot and cut off the string. Discard the thyme and bay leaves. If you'd like the sauce thicker, place the Dutch oven back on the stove and bring to a simmer over medium-high heat. Simmer, stirring occasionally, until the liquid is reduced to the desired thickness (you're looking for a rich and smooth sauce).
To plate, slice the roast into thick slices. Place the vegetables on a platter, then the beef, then ladle the sauce over. Spoon the peas and onions on top and sprinkle with the chives and tarragon.