¼ cup plus 2 tablespoons tablespoon extra-virgin olive oil, plus more for brushing
Preheat the oven to 425°F. Line a baking sheet with parchment paper.
Brush the branzino all over with olive oil and season with salt and pepper. Arrange the fish on the baking sheet and stuff the cavities with the lemon rounds and parsley sprigs. Brush the garlic cloves with a little oil and arrange them on the baking sheet as well. Roast the fish until the flesh is opaque and pulls easily away from the backbone, 15 to 20 minutes. Transfer to a platter.
Squeeze the roasted garlic from the skins into a medium bowl and use a fork to mash. Add the lemon juice and ¼ cup plus 2 tablespoons olive oil. Mix in the chopped parsley. Season with salt and pepper and serve alongside the fish.