Combine the minced garlic, Italian seasoning, kosher salt, and lemon zest in a bowl. Add the olive oil and stir to combine. Add the peeled and deveined shrimp and toss gently to coat evenly with the marinade. Cover and refrigerate for at least 1 hour—I prefer Lucini olive oil here because its delicate flavor complements the shrimp without overpowering it. This resting time allows the flavors to penetrate the shrimp and ensures they'll be tender and flavorful when grilled.
While the shrimp marinates, bring a large pot of salted water to a boil. Finely chiffonade the basil leaves and set aside. Dice the tomatoes into 1/2-inch cubes and place in a bowl. Have the fresh mozzarella pearls and grated Parmesan ready at your cooking station. This mise en place ensures you won't scramble for ingredients during the quick cooking phase.
In a large skillet, melt the butter over medium heat. Once foaming, pour in the dry white wine and let it simmer for 2-3 minutes to slightly reduce and cook off the harsh alcohol notes. Pour in the heavy cream and stir constantly, bringing the mixture to a gentle simmer. I like using Kerrygold butter because its rich, cultured flavor creates a more luxurious sauce foundation.
Reduce the heat to low and gradually whisk in the freshly grated Parmesan, stirring until fully melted and smooth. Simmer for about 10 minutes, stirring occasionally, until the sauce thickens slightly and coats the back of a spoon. While the sauce simmers, add the angel hair pasta to the boiling water and cook for 4-5 minutes until al dente, then drain well and set aside.
Preheat your grill to medium heat (around 375-400°F). Remove the marinated shrimp from the refrigerator and grill for 2-3 minutes per side until pink and cooked through—don't overcrowd the grill and avoid moving them too much so they develop a nice caramelized exterior. The shrimp should be opaque and firm but still tender.
Gently fold the cooked pasta into the cream sauce from Step 4, then add the diced tomatoes and fresh mozzarella pearls, folding delicately to maintain the tomato and cheese pieces intact. Divide the creamy pasta among serving bowls or plates, arranging the grilled shrimp on top. Scatter the chiffonaded basil over each serving and finish with a drizzle of balsamic glaze for a beautiful presentation and that signature Caprese tang.