Heat oil in a large non-stick frying pan over medium-high heat. Add the red and yellow capsicums; sauté until softened, about 4 minutes. Add mushrooms; sauté until vegetables are lightly browned, about 5 minutes. Reduce heat to medium.
Whisk eggs, salt and pepper in a bowl. Pour into pan; cook, stirring frequently, until soft-scrambled, 3 to 4 minutes. Reduce heat to medium-low. Stir in the parmesan and basil; smooth top. Cook 5 minutes. Cover and cook until eggs are firm and bottom is browned, about 8 minutes.
To serve, loosen frittata around the edge with a spatula. Invert onto a large plate and cut into 4 equal wedges. Serve warm or at room temperature.