Place the walnuts in a dry skillet over medium heat.
Toast the nuts for 4 to 5 minutes, stirring often, until fragrant and slightly darker.
Transfer the walnuts to a cutting board to cool, then chop them roughly.
Add the olive oil, apple cider vinegar, honey, fresh ginger, toasted sesame oil, Dijon mustard, salt, pepper, and cayenne to a glass jar with a tight-fitting lid.
Shake the jar vigorously until the dressing is smooth and combined.
Place the baby arugula in a large serving bowl or on a platter.
Arrange the sliced pears and pomegranate arils over the greens.
Drizzle half of the dressing over the salad and toss gently to coat.
Top with the chopped walnuts and crumbled Gorgonzola, adding more dressing if desired.