Preheat your oven to 350 degrees and spray a large baking dish with cooking spray. Set aside.
Cut a pocket into the center of each chicken breast, using a sharp knife,, making sure to not cut all the way through the breast.
Stuff each pocket with 1 oz of goat cheese and sprinkle each breast with a pinch of salt, pepper and garlic powder.
In a large pan, heat 1 Tbsp of olive oil over medium/high heat.
Cook the chicken breasts until lightly golden brown on each side (about 1-2 minutes per side.) Use tongs to flip the chicken as it helps to keep all that cheese inside. However, some cheese may ooze out as it begins to warm up.
Once browned, transfer the chicken to the prepared baking dish and set aside.
Turn the heat down to medium and add the shallots right into the same pan the chicken was in.
Cook the shallots until soft (about 2-3 minutes.)
Add in the balsamic vinegar, pomegranate juice, chicken broth, brown sugar and pinch of salt. Bring to a boil, stiring constantly, until the sauce just begins to reduce and thicken (about 4-5 minutes.)
Pour the sauce evenly over the chicken breasts and bake until they are cooked through (15-20 mins.)
Serve each chicken breast drizzled with some of the leftover sauce, pomegranate seeds and fresh basil.