01 - Heat oven to 425°F and line a baking sheet with parchment paper.
02 - In a large bowl, whisk together flour, baking powder, baking soda, sugar, and salt. Using a pastry blender or fork, cut in cold butter until mixture forms coarse crumbs.
03 - Pour in cold buttermilk and gently mix until just combined. Transfer dough to a floured surface and pat into a 1-inch thick rectangle. Fold into thirds, rotate, and repeat twice for optimal flakiness.
04 - Cut four large biscuits using a 3-inch biscuit cutter. Arrange on lined baking sheet and brush tops with additional buttermilk. Bake 14–16 minutes until golden brown, then let cool briefly.
05 - Pat chicken breasts dry and coat evenly in Cajun seasoning. Heat olive oil in a skillet over medium-high and sear chicken 5–6 minutes per side until cooked through (165°F internal temperature). Rest 5 minutes before slicing.
06 - Whisk eggs, milk, salt, and pepper in a bowl. Melt butter in nonstick skillet over medium heat. Pour in eggs and gently scramble until just set.
07 - Split warm biscuits. Layer with scrambled eggs, sliced Cajun chicken, cheese slices, and green onions if desired. Cap with biscuit lids and serve promptly.