For the balsamic dressing: In a blender, combine the olive oil, balsamic vinegar, Gorgonzola, basil, garlic, a pinch each of salt and pepper and 2 tablespoons water. Blend until the dressing is creamy and the garlic and basil are finely chopped.
For the grilled romaine: Preheat a grill or grill pan to medium heat.
Lightly brush the cut sides of the romaine with the canola oil. Place the romaine on the grill cut-side down and cook until grill marks form and the leaves are slightly charred, 1 to 3 minutes. Arrange on a platter cut-side up.
Drizzle the romaine with the dressing. Sprinkle with the Gorgonzola and torn basil and serve.