Cut off both ends of each of the zucchini. Slice zucchini into 1/4-inch thick slices using a sharp knife or mandoline. Discard the outermost slices and brush both sides of zucchini with olive oil. 

Preheat a grill or grill pan to medium-high heat. Grill zucchini in a single layer for about 2 minutes, flip and grill for another 2 minutes. Cool zucchini and blot with a paper towel to remove excess fluid, if necessary. 

Place cottage cheese in a blender or food processor and blend until smooth, about 45 seconds. Add the Parmesan cheese, lemon juice and black pepper and pulse until just combined.

Spread a thin layer – about 1 tablespoon – of the cottage cheese mixture on each zucchini strip. Place a basil leaf at the end of the zucchini strip, and starting at that end, roll. Repeat with the remainder of the zucchini. Place a toothpick horizontally through the middle of each roll up.  Garnish with fresh basil or chopped chives. 

Use any leftover filling as a dip with fresh vegetables.