Add the pistachios to a food processor or mini chopper. Pulse until finely chopped with a few chunks. Set aside.
Add the ricotta, olive oil, and 1/4 teaspoon of the salt to the food processor. Blend until smooth. Taste and adjust the seasoning, if necessary. Set aside.
Cut the baguette into slices. Place them on a baking sheet. Drizzle evenly with 1 tablespoon of the olive oil, and 1/2 teaspoon of the salt and pepper.
Slice the tomatoes in half. Drizzle on 1 tablespoon of the olive oil and 1/4 teaspoon of the salt and pepper.
Preheat grill to 400° F(200°C). Brush the grill grates clean and spray them with cooking oil.
Add the baguette and tomato slices to the grill and cook for about 2 minutes per side for both. Try to get some grill marks on the tomatoes before they are overcooked and start to fall apart.
Spoon the ricotta mixture onto a serving platter and spread it out with the back of a spoon, forming peaks and valleys.
Drizzle the remaining olive oil onto the ricotta.
Sprinkle with the pistachios (use as many as you see fit and hold back the remaining to sprinkle on again once the original supply is depleted).
Pile the tomatoes on top. Sprinkle on the basil. Serve with the baguette.