Preheat your oven to 400°F (200°C). Cut the top off the head of garlic to expose the cloves, drizzle with a little olive oil, wrap in foil, and roast for about 30-35 minutes until soft and golden. Toss the halved cherry tomatoes with a bit of olive oil, salt, and pepper on a baking sheet. Roast them alongside the garlic for about 20-25 minutes until they start to blister and caramelize.
Bring a large pot of salted water to a boil. Add the linguine and cook according to package instructions until al dente, usually around 9-11 minutes. Reserve about 1/2 cup of pasta water before draining the pasta.
Once the garlic is cool enough to handle, squeeze the softened cloves out of their skins into a bowl. Mash them lightly with a fork. Add the roasted tomatoes (including any juices from the baking sheet) to the garlic, and stir to combine. Pour in the olive oil and mix well.
Add the drained linguine to the bowl with the garlic tomato mixture. Toss gently to coat the pasta evenly, adding reserved pasta water a little at a time if you want a silkier sauce that clings to every strand.
Fold in the chopped fresh basil, then season with salt and freshly ground black pepper to taste. Give it one last toss.
Dish out the linguine onto plates or a large serving bowl. Top with freshly grated Parmesan cheese if desired, and perhaps a few extra basil leaves for color. Serve immediately for the best flavor and texture.
