Remove the dough from the refrigerator to bring to room temperature. Preheat the oven to 475°F. Pat the chicken dry with paper towels; season with salt and pepper on both sides. In a large pan (nonstick, if you have one), heat a drizzle of olive oil on medium-high until hot. Add the seasoned chicken and cook 6 to 7 minutes per side, or until lightly browned and cooked through. Leaving any browned bits (or fond) in the pan, transfer to a cutting board. Carefully chop into bite-sized pieces. Place the choppped chicken in a large bowl; add half the pesto (stirring before adding). Stir to thoroughly coat; season with salt and pepper to taste. 

To the pan of reserved fond, add the tomato sauce (carefully, as the liquid may splatter) and cream (shaking the bottle before opening); season with salt and pepper to taste. Cook on medium-high, stirring occasionally and scraping up any fond, 2 to 3 minutes, or until slightly thickened. Turn off the heat; season with salt and pepper to taste. 

Lightly oil a sheet pan. Using your hands, gently stretch the dough to a 1/4-inch thickness. If the dough is resistant, let rest 5 minutes. Carefully transfer to the sheet pan; rub the dough into the pan to coat the bottom in oil. Leaving a 1-inch border around the edges, evenly top the prepared dough with the sauce and mozzarella cheese (tearing into small pieces before adding). 

Bake the pizza 9 minutes. Leaving the oven on, remove from the oven and carefully top with the dressed chicken. Return to the oven and bake 8 to 10 minutes, or until the cheese is melted and the crust is golden brown. Remove from the oven and let stand at least 2 minutes. 

While the pizza bakes, wash and dry the fresh produce. Cut off and discard the bottom 1/2 inch of the broccoli stem; cut the broccoli into large florets. Place on a separate sheet pan. Drizzle with olive oil and season with salt and pepper; toss to coat. Arrange in an even layer. Roast 18 to 20 minutes, or until browned and tender when pierced with a fork. Remove from the oven. 

While the broccoli roasts, in a large bowl, whisk together the goat cheese, 1 tablespoon of water, and a drizzle of olive oil until smooth. Season with salt and pepper. Roughly chop the almonds. Carefully transfer the roasted broccoli to the bowl of goat cheese; stir to coat. Season with salt and pepper to taste. Evenly top the baked pizza with the remaining pesto. Cut into equal-sized pieces. Serve the finished pizza with the dressed broccoli on the side. Garnish the finished broccoli with the chopped almonds. Enjoy!