Slice the zucchini lengthwise in long, thin slices. You can slice about 16 from 1 zucchini.
Put a cast iron grill pan on high heat. Brush some olive oil on the zucchini slices.
Once the pan is really hot, grill the slices by putting them in the grill pan without any overlap and turn each slice around 3 times (each time after some time to let them acquire a grill mark) to create a nice grill pattern. Place the grilled slices on a paper towel and salt them as soon as they're ready and before starting the next batch.
Artichoke chèvre
In the bowl of your hand blender, briefly grind your grilled artichoke hearts into coarse pieces/shreds. In a separate bowl, mix this with the chèvre by stirring it well with a spoon or fork and season with a little freshly ground pepper.
Mint pesto
Clean the hand blender and then put the fresh basil, fresh mint leaves, pine nuts, Parmigiano and a dash of good olive oil in the bowl of the hand blender to make a pesto.
Zucchini rolls
Then spread the zucchini slices with the goat cheese and artichoke mixture, put a few (thick) drops of pesto over it and roll up the zucchini slices.