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1
Place steak in large pot.
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2
Add enough water to cover steak by 2 inches (about 10 cups).
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3
Add onion, salt, garlic, peppercorns, and bay leaf.
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4
Bring to boil over high heat, skimming any foam from top of cooking liquid.
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5
Reduce heat to medium-low.
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6
Add oregano.
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7
Simmer un-covered until steak is tender, adding more water to cover steak if necessary, about 1 1/2 hours.
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8
Cool slightly.
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9
Refrigerate uncovered until meat and liquid are cold, at least 3 hours and up to 1 day.
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10
Remove steak from liquid, reserving liquid.
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11
Trim excess fat.
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12
Cut steak crosswise into 3 pieces, then shred coarsely.
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13
Transfer beef to large bowl.
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14
Add enough cooking liquid to bowl to cover beef completely.
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15
Whisk vinegar, lime juice, oregano, salt, and pepper in small bowl to blend.
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16
Gradually whisk in oil.
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17
(Shredded beef and vinaigrette can be made 1 day ahead.
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18
Cover separately; chill.
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19
Bring vinaigrette to room temperature and rewhisk before using.)
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20
Combine tomatoes, red onion, and 3 tablespoons vinaigrette in medium bowl; toss to coat.
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21
Season to taste with salt and pepper.
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22
Drain all cooking liquid from shredded beef.
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23
Add lettuce, radishes, and cilantro to bowl with beef.
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24
Mix in enough of remaining vinaigrette to coat.
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25
Season salad to taste with salt and pepper.
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26
Divide salad among plates; surround with tomato mixture.
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27
Garnish with avocado slices.
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28
Serve with corn chips.