In a skillet over medium-high heat, add the butter. As the butter melts and begins to foam, add the Bosc pears. Cook for 2 to 3 minutes until they begin to soften. Add the brown sugar and stir to incorporate the sugar mixture, evenly coating the pears. Stir in the salt, cardamom, and vanilla extract, and continue to stir until the liquid becomes syrupy.
Transfer to a serving bowl and serve over vanilla ice cream garnished with chopped crystallized ginger.