2 tablespoons extra-virgin olive oil, plus more for brushing

1 to 2 jalapeno peppers, seeded and sliced

3 cloves garlic, smashed

1/2 teaspoon dried thyme or 1 1/2 teaspoons fresh thyme

1 medium white onion, minced

1/2 pound skinless, boneless chicken breast, halved lengthwise

Kosher salt

3 to 4 tomatoes (about 1 1/2 pounds), cored and roughly chopped

1/2 teaspoon ground allspice

8 corn tortillas

1 1/2 cups shredded muenster cheese (about 6 ounces)

1 cup mixed fresh parsley and cilantro, chopped