In a stand mixer, combine the instant yeast, sugar, water, and salt. Allow to rest until the yeast begins to foam.
Add the olive oil and bread flour to the bowl and turn the dough hook on low.
Knead the dough for 8-10 minutes, or until all the flour is mixed into the dough and a dough ball is formed.
Either cover and allow the dough to rise for 2 hours or cover and refrigerate for up to 12 hours. (If refrigerating the dough prior to baking, remove from the refrigerator 1 hour prior to shaping.)
Cajun Pizza Sauce
In a small saucepan, melt butter over medium heat.
Add the crushed garlic and cook for 1 minute.
Add the cajun seasoning, tomato paste, and heavy cream to the saucepan.
Simmer the sauce for 10 minutes to thicken, whisking occasionally.
Remove the saucepan from the heat and slowly whisk in the parmesan cheese. Set aside to cool slightly.
Constructing the Pizza
Preheat the oven to 425℉.
Lightly dust a work surface and stretch the dough to a 16-18 inch circle.
Place the dough onto a lightly floured pizza pan and poke holes in the dough using a fork.
Cover the dough with the cajun sauce, spreading out to 1 inch from the outside.
Spread the shredded chicken over the cajun sauce.
Cover the chicken with half of the mozzarella and half of the cheddar cheese.
Evenly spread diced red peppers and green onions over the entire pizza.
Add the rest of the cheeses on top of the vegetables.
Bake the pizza in a preheated oven for 15-18 minutes, or until the bottom crust is browning and the cheese is hot and bubbly.
Remove the pizza from the oven and allow to cool for 5 minutes before slicing.