Preheat: Set the oven to 200°C (400°F)/Gas 6.
Make the butter: Put the butter, garlic, parsley, and a pinch of salt and pepper into a small food processor. Blend until smooth and well combined.
Spread: Lay the baguette halves cut-side up. Spread the garlic butter thickly and evenly over the entire cut surface. Be generous, you want it to melt into the bread, not just coat the top.
Wrap and bake: Press the two halves back together, wrap tightly in foil, and bake for 10 minutes. The foil traps steam so the butter melts deep into the bread.
Unwrap and grill: Open the foil, separate the halves cut-side up, grate the Parmesan evenly over the top, and grill for 2-3 minutes until golden brown and bubbling.
Slice and serve: Cut into thick diagonal pieces and serve immediately while the butter is still molten inside.
