Place the basil, garlic and cheese in a food processor and pulse until coarsely chopped. Pour in the ¼ cup oil and pulse until a smooth sauce forms, adding a little more oil if you find the pistou too thick. Transfer to a bowl and refrigerate until needed.
Set an oven rack six inches below your oven’s broiler. Preheat the broiler to high. Set the baguette slices on a baking sheet. Lightly brush or drizzle them with the 2 Tbsp. olive oil. Broil the bread until lightly toasted. Let the bread cool a few minutes, and then spread with the pistou, set on a platter, and serve.
Note: The baguette used for this recipe was about 2 1/2- to 3-inches wide.