Preheat a grill pan over medium heat for 5 minutes. Slice the bread in half the long way. Brush the cut sides with 2 tablespoons olive oil, season with salt and pepper and grill, cut-side down, until nicely charred. Remove from the grill to a cutting board.
While the bread toasts, toss the tomatoes with a bit of olive oil, salt, pepper and the chopped basil. Mound the mixture on the toasted bread.
Melt the butter in a large nonstick saute pan over low heat. Crack the eggs into a bowl and whisk until light and fluffy with the coarse pepper. Add the eggs to the skillet and mix gently using a rubber spatula until soft curds form. Fold in the cheese and remove from the heat.
Spoon the eggs onto 4 dinner plates. Slice the bruschetta into 4 or 8 pieces and put next to the eggs. Drizzle some olive oil over the bruschetta and scatter the basil leaves on top.