BBQ Chicken and Mushroom Tostadas

Preparation

1. For the Microwave-toasted Tortilla Chips

   1. Step 1

      Cut the tortillas in half or into quarters, or leave whole. Place as many as will fit in one layer on a plate and microwave on full power for 1 minute. Turn over the tortilla pieces (they’ll be wet on the bottom) and microwave again for a minute. The chips should be browned and crisp. If they are not, turn over once more and microwave for another 30 seconds to a minute. Repeat with the remaining tortillas until all of them are done. They’ll remain crispy for several hours. Note: The process will take less time if you air-dry the tortillas on a rack for an hour or so before microwaving.

2. For the Barbecued Chicken and Mushroom Tostadas

   1. Step 2

      Combine the water, the quartered onion and the whole crushed garlic cloves in a 2-quart saucepan and bring to a simmer over medium heat. Add the chicken breasts and bring back to a simmer. Skim off any foam that rises, then add the dried herbs. Partly cover, reduce the heat to low and simmer 15 to 20 minutes, until the chicken is cooked through (cut one in half to check; the meat should not be pink). Add salt to taste. Allow the chicken to cool in the broth if there is time. Remove the chicken from the broth when it is cool enough to handle. Remove from the bone and shred by pulling strips of chicken off the top of the breast, with the grain. You should have about 4 cups of shredded chicken. Strain the chicken broth and refrigerate overnight (the next morning, skim off and discard the fat and freeze the broth in smaller containers).

3. Step 3

   Heat the olive oil over medium-high heat in a large, heavy skillet and add the mushrooms. Cook, stirring, until they are seared and beginning to soften, and add salt and pepper to taste. Continue cooking until mushrooms are just tender, a couple of minutes, and remove from the heat. Add the chicken and the barbecue sauce and stir until the meat and mushrooms are coated lightly with the sauce.

4. Step 4

   Toast the tortillas in the microwave. Toss the arugula with lime juice. Place a spoonful of the chicken and mushroom mixture on the tortillas, top with a handful of arugula, garnish with radishes and serve.