Blackberry Swirl Cinnamon Rolls - Oregon Raspberries & Blackberries

Ingredients

• 2 ½ Cups all-purpose flour
• ⅓ Cup plus 3 tablespoons sugar, divided
• 1 teaspoon sea salt
• 1 package instant yeast
• 6 Tablespoons cold unsalted butter, cut into cubes
• ½ Cup milk
• 2 eggs
• 1 teaspoon pure vanilla extract
• 1 Tablespoon cinnamon
• 2 Cups fresh, frozen (thawed), or canned blackberries, halved if fresh
• 1 Cup powdered sugar
• 2 Tablespoons fresh lemon juice