Preheat the oven to 375 degrees F.
For the hummus: Combine the beans and garlic in a food processor and process until coarsely chopped. Add the peppers, tahini, olive oil and lemon juice, and pulse until almost smooth. Add the parsley, oregano, chile de arbol and some salt and pepper; pulse a few times until just incorporated. Taste, and add a little honey as desired. If the mixture is very thick, pulse in some water; the hummus should be just pourable, more of a sauce than a dip. Transfer to a bowl. (Makes 4 cups; leftovers can be stored in an airtight container in the refrigerator for up to 4 days.)
For the chicken: Combine the paprika, cumin, coriander, salt, pepper, cinnamon, cloves, nutmeg and cardamom in a bowl. Brush the chicken breasts on both sides with canola oil and rub the top side of each breast with some of the spice rub.
Heat a nonstick or enameled cast-iron grill pan over medium-high heat. Sear the chicken, rub-side down, until golden brown and a crust has formed, about 5 minutes. Flip and cook until just starting to brown on the reverse side, another 2 minutes.
Transfer the pan to the oven and cook until an instant-read thermometer reads 160 degrees F, 7 to 10 minutes longer. Remove the chicken to a cutting board and let rest for 5 minutes before slicing.
For the salad: Whisk together the lemon juice, lemon zest, olive oil and some salt in a large bowl. Add the arugula and toss gently.
To assemble: Pile some arugula salad on top of a warm pita, spoon over a generous amount of hummus, and pile on some sliced chicken. Serve warm.