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Cook chicken strips in a nonstick skillet over medium heat for 3 minutes. Preheat oven to 375°F (190°C) with rack in middle position.
In the meantime, combine all pesto ingredients in a food processor or with a hand blender until smooth and consistent. Set aside.
Place naan breads on a baking sheet lined with parchment paper. Spread pesto on naan breads and add chicken strips, then pieces of goat cheese. Cook for 7 to 10 minutes until bottoms of breads are toasted.
Remove from oven, garnish with arugula, and enjoy!
The pizza will keep in the refrigerator without the arugula for up to three days in an airtight container.