Chile-Rubbed Chicken Breast with Kale, Quinoa and Brussels Sprouts Salad

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1 cup dried quinoa

Kosher salt and freshly ground black pepper 

1/2 cup plus 3 tablespoons extra-virgin olive oil 

1 teaspoon ground chipotle powder 

1 teaspoon chopped fresh oregano 

2 small garlic cloves, grated on a rasp, separated 

4 skinless, boneless chicken breast halves 

1/4 cup freshly squeezed lemon juice 

2 tablespoons Dijon mustard 

1 tablespoon minced shallot (from about 1/2 small) 

2 large bunches kale, center stems removed and leaves thinly sliced crosswise (about 1 1/2 pounds total) 

12 ounces Brussels sprouts, trimmed and cored, finely grated or shredded with a knife 

1/2 cup toasted almonds, chopped (about 2 ounces) 

1 cup crumbled Cotija cheese (about 4 ounces)