Preheat oven to 350F.
Turn on burner to medium-low and melt butter in a medium nonstick skillet.
In a separate bowl, whisk together flour and ½ cup milk until completely smooth.
Add flour mixture to skillet followed by the remaining milk (1.5 cups).
Turn skillet up to medium and heat for 7-10 minutes until sauce mixture is thickened. Whisk constantly! If flour begins to stick to bottom remove from heat and turn it down before returning to heat. You will know your sauce is done when you feel some resistance on your whisk.
Remove from heat add in greek yogurt, cheese, and seasonings. Whisk until all the cheese is melted and a smooth creamy sauce is achieved.
In a large bowl combine oatmeal, broccoli, egg, baking soda and cheese mixture.
Once the mixture is well combined add it to a greased 8x8 baking dish or 9 inch cake pan, and bake for 30-35 minutes until it is full set and inserted tooth pick comes out clean.
(Additionally you can broil it for 30 seconds to one minute before removing from oven to get an extra crispy top. )
Let cool for 5 minutes and serve!