Butter a 2 quart flameproof baking dish. Preheat the broiler and arrange a rack on top.
Melt the remaining 2 tablespoons of butter in a small pan over low heat. In a large bowl add the garlic, basil, panko, and 1/4 cup of the Parmesan. Add the melted butter and toss to combine. Reserve.
Bring a large pot of heavily salted water to a boil over high heat. Add the pasta and cook according to the package instructions. Meanwhile, put the half-and-half in a small pot and bring to a simmer over low heat. Simmer until reduced and slightly thickened, about 5 to 7 minutes.
Reserve 1/4 cup of the pasta cooking water and drain the pasta. Put the pot over low heat and add the half-and-half mixture. When it simmers, add the goat cheese and whisk until smooth. Add in the remaining Parmesan and whisk until melted.
Add the pasta and stir to coat. Stir in the pesto, reserved cooking water, salt, and pepper. Season with additional salt and freshly ground black pepper, if needed.
Pour the pasta mixture into the buttered baking dish and top with the panko mixture. Put under the broiler until the mixture bubbles and the top is browned, about 1 to 2 minutes. Remove from the broiler and let cool for 5 minutes before serving.