Preheat a grill pan over medium to medium-high heat.
Discard the outermost slices of zucchini and brush trimmed slices with the oil on both sides and season with a pinch of salt and pepper.
Place on the preheated grill pan for about 3-4 minutes on each side, or until tender.
While the zucchini is grilling, combine the goat cheese, cilantro and dill, mashing with a fork in a small bowl. Season with salt and pepper to taste.
Put a teaspoon of the cheese mixture about ½ inch from the end of a zucchini slice. Roll up and place lay it on a platter. Repeat with the rest of the zucchini slices.