In a large bowl, mix together the flour, Parmesan, baking powder and salt. In a small bowl, whisk the milk, oil and eggs. Add to the dry ingredients and stir just until the batter is combined.
Preheat your waffle iron and spray it with nonstick spray; cook a ladleful (about 1/3 cup, depending on the size of your iron) of batter at a time, and leave it until it stops steaming – cook until deep golden and crisp.
To make the hollandaise, put the yolks, mustard, lemon juice and salt into a blender; cover and pulse until blended. Melt the butter on the stovetop or in the microwave until melted and hot; with the blender on high speed, slowly pour the butter through the hole in the top. It should start to thicken to the consistency of mayonnaise. Once all the butter has been added, scrape the hollandaise out into a bowl and keep at room temperature until serving time.
Top waffles with poached eggs and drizzle generously with hollandaise.