Preheat the grill to medium-high heat.
Add the balsamic to a small saucepan over medium heat and bring to a simmer. Reduce until thickened and syrupy. Set aside.
Toast the pine nuts in a dry saute pan over medium heat for 4 to 5 minutes. Set aside.
Drizzle the eggplant slices with olive oil and season with salt and pepper, to taste. Arrange them on the hot grill. Cook until nicely charred, about 1 to 2 minutes on each side. Remove them to a sheet tray lined with parchment.
Combine toasted pine nuts, goat cheese, heavy cream, salt, pepper and parsley in a medium bowl. Mix well with a wooden spoon, until everything is incorporated evenly. Put 2 to 3 tablespoons of the cheese mixture on the edge of each eggplant slice. Roll the eggplant slices around the cheese. Put the finished roulades back on the grill that has been turned to low. Grill until the cheese begins to melt and the eggplant is warmed through, being careful not to burn the eggplant, about 3 to 4 minutes. Remove the roulades from the grill to a serving platter.
Top each eggplant roulade with a roasted red pepper strip. Garnish with chiffonade of arugula, a drizzle of olive oil and the balsamic reduction.