Start the onions and fennel: Heat olive oil in a cast iron skillet over medium heat until oil covers the pan evenly and is hot. Add the sliced onions and fennel and stir enough to coat with the oil. Continue to cook over medium heat, stirring occasionally until onions and fennel begin to brown, about 10 minutes.
Season with salt and spread onions and fennel evenly over bottom of skillet, reduce heat to low. Allow to gently caramelize for 30 minutes, stirring occasionally to ensure they brown evenly. Stir sliced garlic into onions and fennel; continue to cook on low for another 15 minutes, stirring occasionally. Onions and fennel should be golden brown when done. Remove from heat and allow to cool in pan.
While the onions and fennel are caramelizing:
Pound the thickest part of the chicken breast with a mallet or heavy rolling pin to even out the meat. Season with salt and pepper and a sprinkle of red pepper flakes (optional), on both sides. Drizzle with olive oil to lightly coat. Grill over medium-low heat on a gas grill for 5-7 minutes on each side, depending on thickness, or until the chicken registers 160°F on an instant read meat thermometer. Once done, transfer chicken to cutting board, let rest, tented with foil, 5 minutes, then slice. For this application, it is okay to cook the chicken a little under-done since it will be sliced and then baked in the oven on the pizza.
Roasting Peppers:
Cut pepper in half and remove stem and seeds. Lay pepper on a rimmed baking sheet, skin side up. Roast red pepper, skin side up, under a broiler until skin blisters and is blackened in spots. Remove from oven and place pepper in a sealed plastic bag to cool--the steam in the bag will make it easier to remove the skin. Once the pepper has cooled enough to handle, remove the skin and slice.
Layer pesto, mozzarella, sliced chicken, caramelized onions and fennel, and red peppers on prepared crust and bake for 10-15 minutes in a 450° oven. Allow to rest for a few minutes after removing from the oven before slicing.
Notes
Makes (1) 12-inch pizza.This pizza can be made entirely from scratch or put together quickly using jarred pesto, roasted red peppers, and pre-made grilled chicken breast. The crust does tend to stick to the pan, so it is ideal to line the pan with parchment paper, which the pizza slides off of beautifully when transferring to a cutting board.