Preheat the oven to 425 degrees F. Add the butter and 3 tablespoons olive oil in a medium saucepan over medium-low heat. Stir occasionally until the butter is melted and then add in the oregano, parsley, and minced garlic. Stir occasionally until the garlic is softened (NOT browned), about 2 minutes and then remove from the heat.
Stir in a generous pinch of salt and 1/4 cup finely chopped basil leaves. Slice the french bread in even halves and press the bread down evenly to compress it to 2/3rds the original height. Flip over the bread so the cut side is facing up and place on a parchment or foil lined baking sheet.
Brush half of the garlic herb butter evenly over both surfaces of bread. Place in the oven for 5 minutes, then remove, and set aside.
Meanwhile, return the remaining garlic herb butter to the stovetop and add in the tomatoes. Stir and then increase heat to medium, bring to a simmer, then reduce heat to maintain a slow simmer. Cook, stirring occasionally, until reduced, about 10 minutes. Season to taste with salt and pepper.
Spread sauce evenly over the two bread halves, and then spread mozzarella cheese on top. Add the thinly sliced roma tomatoes evenly to both halves. Bake for another 8-12 minutes or until cheese is melted and the bread is lightly browned at the edges.
Remove from the oven and sprinkle the parmesan cheese evenly over the tomatoes. Add fresh basil (rip or add full leaves), some freshly cracked pepper, and drizzle the last tablespoon of olive oil over everything. Enjoy immediately.