Preheat the broiler.
Coat a large skillet with 4 seconds of cooking spray. Add half the garlic and half the onion and a pinch of red pepper flakes, place over medium high heat and cook until softened, about 2 minutes. Add in half the chicken broth, all of the tomato purée and the diced tomatoes and bring to a simmer. Reduce the heat to low and simmer for 30 minutes.
Place the eggplant, cut side up on a broiler pan and broil until lightly browned, 4-6 minutes. Remove the eggplant from the broiler, place it on a microwave-safe plate and microwave on high until tender, about 2 minutes. Let cool.
Scoop the eggplant pulp out of its skin and let any excess water drip off. Measure out 1/2 cup of the pulp, then chop it fine.