Preheat oven to 350ºF. Coat a 9x13-inch baking dish with butter or spray well with non-stick baking spray. Set aside.
Beat butter until creamy with an electric mixer. Add brown sugar and granulated sugar and mix until light and fluffy, about 3 minutes. Add eggs and vanilla extract and mix until well combined. Stir in flour, oats, salt, and baking soda until well combined. Spread the batter evenly into the prepared 9x13 baking dish and set aside.
Add brown sugar, heavy cream and cinnamon to a small saucepan set over medium-low heat. Stir together to combine with a wooden spoon. Add the butter and allow to melt completely and for the mixture to reach a rolling boil. Allow to cook until the sauce thickens, about 3 minutes. Remove from the heat and stir in the vanilla.
Drop the cinnamon sauce onto the top of the blondie batter by the tablespoon. Swirl into the batter with a skewer or butter knife.
Bake until set in the middle and lightly golden brown, about 30 minutes. Cool completely before cutting and serving.