3 1/2 lbs top blade steaks (or boneless chuck roast), 1-inch thick, trimmed of gristle and fat and cut into 1-inch pieces
Salt and pepper
3 Tbsp vegetable oil
2 lbs yellow onions (about 3 medium), halved and sliced about 1/4-inch thick
1 Tbsp tomato paste
2 medium garlic cloves, minced
3 Tbsp AP flour
3/4 cup low-sodium chicken broth
3/4 cup low-sodium beef broth
1 12-oz bottle or can of beer
4 sprigs fresh thyme, tied together with kitchen twine
2 bay leaves
1 Tbsp cider vinegar
Adjust oven rack to lower-middle position and heat oven to 300. Dry beef thoroughly with paper towels and season generously with salt and pepper. Heat 2 teaspoons of the oil in a Dutch oven over medium-high until almost smoking. Add about a third of the beef to the pot, and cook without moving pieces for 2-3 minutes. Flip pieces over with tongs and coook for another 2-3 minutes. Transfer the browned beef to a bowl, and repeat with the other two-thirds of the beef, adding more oil if necessary.
Add 1 tablespoon of oil to the pot and lower the heat to medium-low. Add onions, tomato paste, and some salt. Scrape the bottom of the pot with a wooden spoon or spatula to loosen the fond. Cook, stirring occasionally, until onions have released some moisture, and raise the heat to medium. Continue to cook until onions are lightly browned, 12 to 14 minutes. Add garlic and cook until fragrant, about 30 seconds. Add flour and stir until onions are evenly coated and flour is lightly browned, about 2 minutes. Stir in broths, scraping the bottom of the pot, then add beer, thyme, bay, vinegar, and the beef (with any accumulated juices). Add salt and pepper to taste. Increase heat to medium-high and bring to a simmer, stirring occasionally. Cover partially, then place pot in oven. Cook until fork inserted into beef meets little resistance, about 2 hours.
Discard bay and thyme. Adjust seasoning with salt and pepper. Serve over buttered noodles or mashed potatoes.