Cheesy Pull Apart Bread – Fustini's Oils & Vinegars

Ingredients

• 1 3/4 cups all-purpose flour
• 1 cup whole wheat pastry flour
• 1 tablespoon sugar
• 2 1/4 teaspoons instant yeast (1 envelope)
• 1/2 teaspoon salt
• 1/3 cup milk
• 6 tablespoons Fustini's Pesto olive oil, divided, plus more for oiling bowl
• 1/4 cup water
• 2 eggs, at room temperature
• 12 ounces sharp cheddar cheese, freshly grated (1 1/2 bricks)