Brown the beef. Preheat a heavy-based soup or stew pot over medium-high heat. Add the oil. When wisps of smoke begin rising from the oil, working in batches, brown the beef thoroughly. Little by little, this should create a fond, or caramelized bits of meat, on the bottom of the pot. Continue working in batches to not crowd the beef. Adding too much beef at once will cause it to steam rather than brown. Add oil as necessary. Once the beef is browned, transfer it to a clean plate.
Add tomato paste and cook it off. Reduce the heat to medium. Add the tomato paste to the pot. Cook it off for 3-5 minutes. This allows you to extract maximum flavor from the tomato paste.
De-glaze with beer. At this point, there should be a char consisting of browned beef and tomato paste on the bottom of the pot. De-glaze with a splash of brown beer. DO NOT discard this. This char, or fond as it's called, is where much of the stew's flavor is going to come from.
Cook the onions and garlic. Add the butter to the pot, along with the onions and garlic. Cook 3-5 minutes.
Add the flour, stirring constantly to cook it off.
Add the vegetables and potatoes. Mix well to combine. If the pot is getting dry, add a bit more extra virgin olive oil.
Add remaining beer, beef stock, and water. The vegetables should be just slightly covered by liquid. Mix well to deglaze any remaining, or newly formed, fond from the bottom of the pot. *
Return the beef to the pot.
Add the herbs.
Let cook for 2-3 hours. Cover, lower the heat, and bring the stew to a simmer. Cook low and slow for a minimum of 2 hours. After 2 hours, remove the lid, and simmer for another 30 minutes. This will allow the sauce to reduce, further thickening the stew.