In a large saucepan, over medium heat, melt the butter. Stir in the sugar and cinnamon, stirring until the sugar dissolves. Add the pears and salt. Mix well. Cook for 4 minutes, stirring occasionally. Dissolve the cornstarch in the water. Stir the cornstarch slurry into the pears and continue to cook for 2 minutes. Remove from the heat and cool completely.
Place 1/2-ounce of the blue cheese and 1/2-ounce of the Brie over half of each tortilla. Fold the tortillas over and press firmly. In a large saute pan, over medium heat, add 1 tablespoon of the oil. Add a few of the quesadillas and pan-fry for a couple of minutes on each side until golden brown and the cheese is melted, making sure not to crowd the pan. Pan-fry the rest of the quesadillas in small batches.
Fry the walnuts for 1 minute. Remove and sprinkle with cinnamon sugar mixture. Drain on paper towels. Slice the quesadillas in half and serve with the pear compote and walnuts.