Drain oil from sun-dried tomatoes, reserving 3 tbsp.

Combine sun-dried tomatoes, minced garlic, Parmesan, salt, and reserved oil in a blender.

Blend until finely chopped, scraping down sides as needed.

Add pine nuts and basil; pulse until incorporated but still visible.

Refrigerate pesto until needed.

Cut each bocconcino into 4 slices.

Stir softened butter with minced garlic and parsley.

Butter one side of each slice of bread.

Spread a thin layer of pesto on the dry side of half of the bread slices.

Top with sliced bocconcini, dividing equally.

Cover with remaining bread slices, dry side towards cheese.

Heat a large frying pan over medium-low heat.

Cook sandwiches in batches, pressing down with another frying pan.

Grill for 8-10 minutes, checking underside until golden brown.

Flip sandwiches; replace the frying pan weight.

Continue grilling for 6-8 minutes, or until golden and cheese starts to ooze.

Cut sandwiches in half; serve immediately.