In a medium bowl, stir together the softened butter, light brown sugar, and cinnamon until smooth. Transfer the mixture to a pastry bag or a plastic zip-top bag with one corner snipped off for piping. Set aside.
In a large bowl, whisk together the flour, baking powder, and kosher salt.
Add the buttermilk, egg, vanilla extract, and vegetable oil to the dry ingredients. Whisk until just combined and smooth, without overmixing. Set aside to rest while you make the icing.
In a small bowl, use a hand mixer or whisk to blend the softened butter and cream cheese until creamy and smooth. Add the confectioners' sugar and vanilla extract. Mix until fully combined and the icing is smooth and pourable. If needed, thin with a teaspoon of milk for drizzling consistency. Set aside.
Heat a nonstick skillet or griddle over medium heat. Lightly coat with cooking spray.
Scoop ⅓ cup of batter onto the skillet for each pancake. Gently spread the batter into a circle about 3-4 inches wide.
Reduce the heat to medium-low. When bubbles begin forming around the edges of the pancake, pipe a swirl of the cinnamon filling onto the surface, starting from the center and spiraling outward.
Cook the pancake for 2 to 3 minutes, or until bubbles begin popping and the bottom is golden brown. Carefully flip the pancake and cook for another 2 to 3 minutes, until the other side is golden and the cinnamon filling is slightly caramelized.
Wipe out the skillet with a paper towel between batches to prevent the filling from burning. Repeat with the remaining batter and cinnamon filling.
Serve warm pancakes drizzled generously with the cream cheese icing.