Bring a large pot of salted water to a boil and cook the penne until just shy of al dente according to package directions. Reserve 1/2 cup of the starchy cooking water, then drain the pasta and set aside.
Pat the shrimp dry and toss with 1/4 teaspoon salt and black pepper. Heat 1 tablespoon olive oil in a large skillet over medium-high heat until shimmering.
Sear the shrimp in a single layer, 1 to 1 1/2 minutes per side, until pink and just cooked through. Remove the shrimp to a plate and keep warm; leave any juices in the pan.
Lower the heat to medium and add the remaining 2 tablespoons olive oil to the skillet. Add half the minced garlic and the sun-dried tomatoes; sauté for about 1 minute until fragrant, using a wooden spoon to scrape up brown bits.
Pour in about 1/4 cup of the reserved pasta water to deglaze the pan, then stir in the half-and-half. Bring the mixture to a gentle simmer.
Remove the skillet from the heat briefly and add the shredded mozzarella in small handfuls, stirring steadily until it melts into a smooth sauce. Return to very low heat and simmer 2–3 minutes; if the sauce seems too thick, whisk in more reserved pasta water by tablespoons.
Stir in the remaining garlic, dried basil, red pepper flakes, lemon zest, and 1/2 teaspoon salt. Taste and adjust seasoning as needed.
Add the drained pasta to the sauce, tossing gently to coat. Return the seared shrimp to the pan and fold everything together. Let the pasta sit off the heat for 1–2 minutes to thicken slightly and allow flavors to meld.
Divide among plates and finish with an extra pinch of red pepper flakes or a few basil leaves if desired. Serve immediately.