Cut the Comté cheese into strips. Put half of it on 4 slices of bread. Add the white ham and the rest of the comté. Cover with the other slices of bread.
Melt the butter over very low heat and brush it on the croque-monsieur. Place on a baking sheet.
Place under the broiler for 6 minutes, turning halfway through cooking
Once out of the oven, cut each croque-monsieur lengthwise into 4 pieces. Arrange the truffle pesto and truffle strips on top and serve immediately.