In a small bowl, stir together the honey mustard and pineapple jam. Divide the mixture evenly between 4 of the tortillas. Spread evenly to within 2.5cm of the edges. Distribute the Gruyere cheese, chicken, bacon evenly over the pineapple mixture then top with remaining tortillas to make quesadillas.
Preheat the oven to 120 degrees C.
Heat a large frying pan over medium heat. Melt a small amount of the butter in the frying pan, tilting the pan to cover the surface with butter. Place one of the quesadillas into the frying pan; fry on each side until lightly browned and the cheese has melted, about 1 1/2 minutes per side. Keep cooked quesadillas in a warm oven while you fry the remaining.
To serve, cut each quesadilla into 6 wedges and arrange on a platter with pineapple bits in the centre.
If your local supermarket doesn't stock it, you may find it online, otherwise you can substitute with apricot jam.