Preheat oven to 400°F (200°C). Line a baking sheet with parchment paper and set aside.
Cook the sweet potatoes until very tender when pierced with a fork; 8–10 minutes. Alternatively, microwave in a bowl with ¼ cup water, covered, until tender; for 5 minutes. Drain. Transfer to a large bowl and mash until completely smooth. Set aside and let cool in room temperature.
Add in the flour, eggs, salt, and stir to combine. Place the mixture on the prepared baking sheet and spread it into a 12x10x½-inch (30cmx27cm) rectangle. Bake until the base is dry to the touch and beginning to brown on the edges; about 25 minutes.
Spread the tomato paste and barbecue sauce evenly on the pizza base. Place chicken, onions, and bell pepper evenly on the top and bake for 10 minutes. Remove from the oven and sprinkle with cheese. Continue baking until the cheese is bubbly; about 10 minutes. Cut into squares and serve.