For Tomato Oil & Solids: Combine all ingredients such as tomato paste, canola oil, olive oil, 1 tbsp pepper and 1 tsp salt in saucepan. Bring to a boil; reduce heat and simmer gently 15 minutes, stirring occasionally. Let cool. Pour into nonreactive container. Refrigerate, covered, overnight.
Carefully remove oil that has risen to top of tomato solids. Reserve both oil and solids.
For Veal Rolls: Place veal cutlet on parchment paper; season with 2 tsp salt and 2 tsp pepper. Spread 2 tsp tomato solids over surface. Top with 1 tbsp basil. Layer 1 slice prosciutto and 2 cheese half-slices over basil. Roll cutlet into tight roulade. Skewer 1 green onion piece onto two 3-inch soaked wooden toothpicks or skewers; secure roulade with picks.
Veal rolls can be made ahead, tightly covered with plastic wrap and refrigerated until service.
Grill veal rolls over medium heat 13 to 15 minutes for medium doneness (160°F), turning frequently (about every 2 minutes) to brown all sides.
Drizzle plate with 1 tbsp tomato oil and top with 2 veal rolls. Serve with lemon half.