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1
Put chicken in a skillet or saucepan and add enough water to cover, bring to a simmer over high heat.
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2
Cover, reduce heat and simmer gently until the chicken is cooked through and no longer pink in the middle, 10 to 12 minutes.
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3
Transfer to a cutting board.
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4
When cool enough to handle, shred with two forks into bite-size pieces.
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5
Bring a large pot of water to a boil, add broccoli and cook until tender, 3 to 5 minutes.
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6
Drain and rinse with cold water until cool.
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7
Meanwhile, core tomatoes and cut in half crosswise.
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8
Gently squeeze out seeds and discard.
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9
Set the tomatoes cut-side down on paper towels to drain for about 5 minutes.
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10
Place a large heavy skillet, such as cast-iron, over high heat until very hot.
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11
Brush the cut sides of the tomatoes with 1 teaspoon oil and place cut-side down in the pan.
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12
Cook until charred and beginning to soften, 4 to 5 minutes.
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13
Brush the tops lightly with another 1 teaspoon oil, turn and cook until the skin is charred, 1 to 2 minutes more.
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14
Transfer to a plate to cool.
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15
Do not clean the pan.
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16
Heat the remaining 3 tablespoons oil in the pan over medium heat.
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17
Stir in salt, pepper and chili powder and cook, stirring constantly, until fragrant, about 45 seconds.
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18
Slowly pour in lemon juice (it may splatter), then remove the pan from the heat.
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19
Stir to scrape up any browned bits.
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20
Coarsely chop the tomatoes and combine them in a large bowl with the shredded chicken, broccoli and the pan dressing; toss to coat.
