In a large sauté pan or skillet, cook onions over medium heat stirring often until softened and translucent, about 8-10 minutes. Stir in garlic, cumin, chili powder and sugar until the spices are fragrant, about 20 seconds.
Add the chopped tomato, tomato sauce, water, sofrito and adobo (or salt and pepper) to taste. Reduce the heat to medium/low and bring the sauce to a simmer for about 2 minutes.
Reduce the heat to low and add the chicken to the sauce. Cover the chicken and cook until the chicken is completely cooked, about 20-22 minutes. Remove chicken from the saucepan, and transfer to a plate. Set aside to cool slightly.
Strain the sauce from the pan through a mesh strainer into a medium bowl, pressing down on the onions and tomatoes to extract as much liquid as possible. Transfer the solids to a large bowl and set aside. Add additional adobo (or salt and pepper) to the sauce if needed. Add the sauce to a saucepan and cook, reducing by about half over medium/high heat, about 5-7 minutes. If needed, lightly salt and set aside to cool.
Shred the chicken into bite size pieces and add to the bowl with the reserved solids. Add in 2 tablespoons of the reduced enchilada sauce and the cilantro. Stir to combine. Set aside remaining reduced enchilada sauce for the pizza.
To assemble the pizza
Preheat the oven to 500 degrees Fahrenheit. Brush a rectangular cookie sheet with olive oil, and then dust with a coating of semolina flour or whole wheat flour. This will prevent the dough from shrinking on itself (pro tip).
Place pizza dough in the center of the cookie sheet and roll or lightly pull/stretch the dough to cover the entire cookie sheet. If the dough gets tough to stretch or roll, allow it to rest for a few minutes and continue rolling until you are able to cover the cookie sheet.
Once the pizza dough is rolled, lightly brush outer edges with olive oil. I like to also lightly sprinkle the edge of my dough with a little salt (or garlic salt), but you can leave as is.
Place the pizza dough in the oven and bake for about 10 minutes until the pizza dough is a very, very light golden color. The dough should have lost its shine, but should not be dark. At all!
Remove pizza dough from the oven (be careful, it’s hot!) and add the shredded chicken mixture. Add the shredded cheeses and diced tomatoes. Dot the pizza dough with remaining reduced enchilada sauce. Top with additional cilantro, if desired.
Place pizza dough with toppings back in the oven and bake until the cheese is bubbling and the crust is lightly browned, about 12-15 minutes.