Preheat oven to 500°F/260°C.
Trim off any excessive fat from the center of the chuck. Cut the rest of the meat into cubes. You should be left with about 3½ lb/1½ kg of meat.
Add meat cubes to a bowl and drizzle with generous amount of olive oil and 2 large pinches of salt. Toss to coat and spread beef onto a half sheet tray and load into 500°F/260°C oven to sear for about 20-25 minutes until well browned.
Reduce oven temperature to 300℉/150℃.
Preheat a large heavy-bottomed pot over medium-high heat. Add a generous glug of olive oil followed by mushrooms, carrots, onions, and a pinch of salt.
Sweat the veggies to par-cook for 3-5minutes until it's beginning to soften and caramelize. Transfer veg into a bowl and set aside.
Return pot to stove over medium heat and add 1 stick/115g butter.
When the butter is melted, add 100g/¾ cup of flour. Stir to cook, scraping up brown bits from bottom of the pot. Fry for 60-90 seconds until smooth and taking on color.
Pour in beef stock and beer. Bring the pot to a simmer, stirring and scraping frequently. Once simmering, add in the chunks of beef.
Add a splash of water to the beef cooking tray, scraping up any beef fond with a wooden spoon. Marry the fond water into the pot with the beef. Stir to combine.
Load pot, uncovered, into a 300°F/150°C oven and cook for 2 hours, stirring halfway through.
Toss potatoes into a mixing bowl with the par-cooked vegetables and mix with 25g/3tbsp flour. Toss to combine. (NOTE: if your stew is relatively thick at this point, omit tossing the veg in the flour or add less flour here).
Remove stew pot from oven and carefully add the potatoes/veggies into the stew. Gently stir and add in bay and thyme.
Return stew pot to the oven uncovered to cook for 1 more hour.
At this point, check the beef and potato for doneness. Beef should be tender and shreddable, but not shredded. Potato should be fork tender, but not mushy.
Ladle off excess fat from top of stew (or allow to cool slightly, refridgerate, then scrape off fat from top once cooled). Stir peas into hot stew.
Taste for seasoning and add salt if needed.
Ladle into bowl, top with fresh cracked black pepper, and serve with a piece of rustic sourdough bread.