To prepare the pesto, combine basil, garlic and pine nuts in a food processor container.
Pulse until coarsely ground. Slowly add the olive oil and blend until the mixture becomes smooth.
Transfer to a large bowl and season with salt and pepper.
Stir in grated cheese until thoroughly combined.
Freeze unused portion in ice cube trays and top with additional olive oil. Use frozen pesto cubes in soups or stews for additional flavor, as needed.
Slice the heirloom tomato into a few thin slices
Cut the French rolls in half lengthwise and butter the inside portion of both halves.
Place buttered side down on grill pan heated over medium-high heat. Press down on the outside of the roll to achieve even grill marks.
When golden brown, remove from heat and spread a generous amount of pesto on the warm, grilled portion of each piece.
Heat turkey in the microwave with a little bit of chicken or vegetable stock until warm.
Add turkey and Provolone cheese to each roll.
Top the cheese with one slice of tomato and a handful of arugula.
The heat from the turkey and the grilled roll should melt the cheese. Serve immediately.