Preheat oven for 425 degrees F. Line a baking sheet with parchment paper. Slice a grid pattern into the loaf of bread, leaving about an inch uncut at the bottom of the loaf. I find it easiest to slice longways and then go back and slice the rest of the grid.
Loosely tent the bread with foil and place in the oven for 10 minutes.
Melt the butter in the microwave or a small saucepan. Immediately add the garlic cloves to the butter, stirring well. Add in the parmigiano reggiano and the thyme leaves, stirring once more. Gently pry apart the bread squares and drizzle the butter into the crevices of the bread. Once you’re finished with the butter, gently add the chopped sun dried tomatoes down into the crevices of the bread too. Mix all the grated cheeses together and again, gently pry apart the bread and stuff the cheese into the crevices and pile it on top.
Bake the bread for 15 to 20 minutes, uncovered, or until the cheese is golden and bubbly. Remove the bread and sprinkle some extra parmigiano reggiano on top. Add the fresh basil leaves. Serve immediately.