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Toss chicken thighs with two tablespoons of oil, garlic, rosemary, and salt. Cover and allow the chicken to rest for thirty minutes at room temperature, or in the refrigerator for four hours or more.
Melt butter and remaining tablespoon of olive oil in a large, deep skillet. Add thyme, vinegar, sugar, onions, and pepper. Cook over a low heat, stirring periodically, until onions have softened. Add water on occasion to keep onions from drying out.
Grill chicken over moderately high heat in a gas, charcoal, or electric grill until cooked through and lightly charred. Allow to cool, and then pull from bones and shred.
On two large baking sheets, arrange six of the tortillas and spoon onions onto each. Top with chicken and blue cheese, then cover with remaining tortillas and press to flatten. Bake for six minutes, or until tortillas are toasted and golden. Serve individually, or cut into wedges.
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