Add drizzle of olive oil to a large dutch oven and heat over MED-HIGH heat. Add beef and brown, about 5 minutes, using a wooden spoon or silicon coated potato masher to break up into crumbles.
Transfer cooked and crumbled beef to a bowl, and return pan to heat. Add onion and poblano peppers to pan and saute, stirring occasionally, about 5 minutes, until soft. Add garlic and cook another 30 seconds or so.
Transfer cooked beef back into pan, add seasonings (chili powder, ancho Chile powder, cumin and salt), stirring to combine. Cook about 30 seconds.
Add tomato paste and stir into the meat mixture. Pour in beer, using wooden spoon to scrap the bottom of the pan to bring up any browned bits (big flavor!). Cook about 2 minutes.
Pour in 1 1/2 cups of beef stock, bringing to a boil. Combine remaining 1/2 cup beef stock and all purpose flour, using a fork or small whisk to combine fully.
Pour flour mixture into pan, stirring constantly, until full incorporated. Stir in oregano and tomatoes, bring to a boil.
Reduce heat to LOW or MED-LOW (depending on your stove), cover with lid almost all the way (I leave mine cracked about 1/2 inch), and simmer 40-45 minutes.
Remove pan from heat, ladle into bowls, top with desired toppings and enjoy!