Clean and oil your grill grate. Turn on and heat to medium high heat.
Cut pears in half and scoop out the cores. Slice a piece off the skin side so it will lay flat without rolling. Brush with a light oil (see Recipe #369334). Place pears cut-side down on the grill. Cover and cook until heated through and nice grill marks appear, about 10 minutes.
In the meantime, toast walnuts in small pan over medium heat on stovetop until toasted, about 5 minutes. Pour walnuts in small bowl and while still warm add gargonzola and mix so cheese melts. Add honey. Stir lightly to incorporate.
Toss arugula or other greens very lightly with vinaigrette. Divide onto four plates.
When pears are nicely grilled on cut side turn over and divide gorgonzola mixture among pears. Grill for a couple minutes more. Remove pears and place ½ pear on each of the four plates. Drizzle with vinaigrette. Serve warm.