Roast Garlic: Preheat the oven to 350°F (176°C). Slice the top of a head of garlic off so that the cloves are exposed and gently rub your fingers back and forth over the sides to remove as much of the paper as you can. Drizzle the cloves with olive oil, and wrap the head tightly in aluminum foil. Roast the garlic until the cloves are caramel in color, about 45 minutes. Allow the garlic to cool completely before squeezing out the cloves. Set aside.
Marinate the Chicken: For the chicken, add the chicken to a large baking dish or resealable plastic bag. Whisk together 3 tablespoons (45 mL) of the olive oil, the lemon zest, and juice, garlic, dill, vinegar, honey, salt and pepper. Pour it over the chicken and toss it to coat. Place the dish or bag in the refrigerator and marinate for at least 2 hours or overnight.
Prep Tzatziki: While the chicken is marinating, prep the tzatziki. Combine all of the ingredients together in a large bowl and mix them together until combined. Store the dip in the fridge until ready to use.
Prepare the Whipped Feta: For the whipped feta, preheat the broiler in your oven to high and move an oven rack directly below it. Place the jalapeño peppers on a baking sheet. Once the broiler is hot, set the baking sheet underneath to roast the peppers. As soon as the skin begins to char and bubble, pull the baking sheet out and rotate the peppers to roast all sides. This should take about 5 minutes. Immediately remove the peppers and place them in a resealable plastic bag (note: or bowl covered with plastic wrap) for 20 minutes. The bag will steam up.
After 20 minutes, remove the peppers from the bag and gently push and peel the charred skin on the peppers to remove it. Slice the tops of the peppers off and cut them in half. Remove the seeds and cut the peppers into pieces.
Add the feta cheese and cream cheese, if using, to a food processor. Puree until the cheese are completed blended and smooth, then add the chopped jalapeño peppers, the roasted garlic cloves, the lemon zest and juice, and the salt and pepper. Blend again until all of the ingredients are combined. If you are serving the dish within the next 2 hours, the feta can sit at room temperature. Otherwise, store it in a sealed container in the fridge and set it out an hour before serving.
Prepare Pitas: For the pitas, remove the chicken from the marinade and discard the juices. You can cook the chicken any way you like–I find the quickest method to be heating a large skillet over medium heat and adding the remaining 1 tablespoon of olive oil. Put the chicken in the skillet and cook it until golden and brown on both sides, 10 minutes per side. Remove the chicken from the skillet and let it rest for 1 to 2 minutes. Cut it into pieces or shred it.
Assemble the pitas by heating the pitas in the oven or microwave for a minute or two. Spread the feta dip on the pitas, then top with chicken, lettuce, tomatoes, cucumbers, red onion, hummus, and tzatziki.