In a small bowl, combine goat cheese and basil until mixed. Set aside or allow to sit in the fridge.
Combine flour and yeast in a large bowl. Add water, honey and oil, mixing with a spoon to form into a ball. Just before it comes together, add in salt and mix. If needed, add more water 1 tablespoon at a time. Continue mixing with your hands and knead for about 60 seconds. Lightly oil the bowl and add dough back in. Cover and let rise for 2-3 hours.
After 2-3 hours, remove from bowl and punch down. Roll back into ball and let sit for 30 minutes.
Lay on a lightly floured surface and roll very thin. Along the outer edge (about 1 1/2 inches from the outside) place goat cheese around the entire outside. Fold dough over top and press down to seal the top to the bottom. Top with desired toppings and bake at 375 degrees for 25-30 minutes.