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Fill a large pot halfway with water and add chuck roast. Add onion and 4 cloves garlic, and season with salt. Cook over medium-low heat until meat is falling apart, about 1 1/2 hours. Let cool slightly and shred using 2 forks. Set aside and keep warm.
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Bring water to a boil in a large pot; add pinto beans and salt to taste. Reduce heat to medium-low and cook until tender, about 1 hour. Drain and let cool slightly. Smash beans using a potato masher; set aside and keep warm.
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Place red onions, vinegar, lemon juice, salt, and pepper in a bowl and combine. Cover and refrigerate until ready to use.
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Bring tomatoes, jalapenos, and enough water to cover to a boil in a small pot. Continue to boil until semi-soft, 8 to 10 minutes. Let cool slightly and transfer to a blender. Add remaining 2 cloves garlic; season with salt. Blend hot sauce until smooth.
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Top each tostada evenly with cooked beans, sour cream, shredded beef, lettuce, Cotija cheese, marinated red onions, and hot sauce, in that order.
Cook’s Notes:
Both the roast and beans can be prepared a day or so beforehand.
If you are frying your own tostadas, use a frying pan with plenty of oil over high heat. Once the frying pan is hot, place a corn tortilla into the pan, pressing down with a large cooking utensil, not allowing the tortilla to get bubbly. Cook until nice and crispy, about 2 minutes on each side.