Preheat oven to 450 degrees F (230 degrees C). Brush a 9x13-inch baking dish with olive oil.

Stir hot roll mix and the yeast packet from the box together in a large bowl. Add hot water, butter, and egg; stir until dough pulls away from the sides of the bowl.

Turn dough out onto a lightly-floured surface and knead until smooth, about 5 minutes. Spread dough into prepared baking dish, cover with plastic wrap, and let rise until doubled in volume, about 30 minutes. Press dimples into the top of the dough with your fingertips.

Scatter crumbled sardines over the top of the dough, sprinkle garlic over sardines, and top with Parmesan cheese.

Bake in the preheated oven until golden and fragrant, about 30 minutes.