Make the waffles:

1. Heat the oven to 250°F.  Prepare a sheet pan with a wire rack on it.  Place this in the middle rack of the oven.  You will use this to keep the finished waffles warm.
2. Whisk together flour, baking powder and salt in a large bowl.
3. In another large bowl, whisk eggs gently, add milk, and slowly pour in the melted butter while whisking constantly.  Whisk until evenly combined, and then stir in the shredded cheese.
4. Add the wet ingredients to the dry ingredients, and stir with a silicone spatula until flour is just incorporated.  There may still be a few lumps in the batter.
5. Heat the waffle iron according to manufacturer’s instructions.  Spray with nonstick cooking spray.  Pour enough batter to just cover the waffle grid.  Close, and cook until golden brown, about two to three minutes. 
6. Transfer the finished waffles to the wire rack in the oven to keep warm.  Garnish with scallions and a spoonful of compote.  Serve immediately.

Make the compote:

1. In a 10 inch skillet over medium heat, melt the butter.  
2. Stir in brown sugar and cinnamon until the sugar dissolves, about 1 minute.
3. Add the apples, pears and salt.  Stir to coat the mixture.  
4. Cook the mixture down for 4 minutes, stirring occasionally until fruit is slightly softened.
5. Dissolve the cornstarch into the cognac, and stir to make a slurry.  Pour the cornstarch slurry into the fruit.
6. Continue to cook for a couple of minutes until the mixture thickens.
7. Remove from the heat, and allow the compote to cool slightly before serving on top of your waffles.