In a saucepan set over medium heat, add 1 tablespoon of olive oil, garlic and red pepper flakes, stirring until fragrant, about 30 seconds.
Stir in the spinach and artichokes.
Mix in the cream cheese, sour cream, ½ of the mozzarella and Parmesan. Stir until combined and cheese has melted.
Season with salt and pepper. Remove from heat and set aside.
Preheat oven to 375°F (190°C).
Remove the top of the sourdough boule. Cut around the inside of the bread, being careful not to cut through the sides, and scoop out the center of the boule.
Cut the scooped out bread into cubes, and place on a baking sheet lined with parchment paper.
Vertically slice into the edges of the bread bowl, cutting all the way through the bottom, leaving 1 inch (2 cm) of space between each. Place onto a baking sheet next to the cubed bread.
Spoon the spinach artichoke mixture into the sliced and hollowed bread bowl. Sprinkle the remaining mozzarella along the edges of the top of the filled bread bowl.
Drizzle the cubed bread pieces with the remaining tablespoon of of olive oil. Place the sliced top back onto the bowl.