Preheat the oven to 425°F (220°C). Spray a 9-inch springform pan with nonstick spray and, if desired, wrap the outside bottom edges with foil to prevent leaks.
Bring a large pot of salted water to a boil and cook the bucatini 1–2 minutes less than the package directions so it remains al dente. Drain the pasta and let it cool slightly; toss with a little olive oil if it looks likely to stick.
In a large bowl, whisk together the whole milk, grated Parmigiano-Reggiano, beaten eggs, minced garlic, kosher salt, and a pinch of freshly ground black pepper until smooth.
Stir in 1 cup of the grated provolone and half of the grated mozzarella, then fold in 3/4 cup of the pesto until combined.
Add the drained bucatini to the bowl and toss gently until all pasta is coated in the cheese-and-milk mixture.
Transfer the pasta mixture to the prepared springform pan and spread into an even layer. Sprinkle the remaining provolone and mozzarella over the top and drizzle extra pesto as desired.
Bake for 35–45 minutes, until the cheese is golden and bubbly and the center is set.
Remove from the oven and cool 10–15 minutes. Run a sharp knife around the edge if needed, release and remove the springform ring, slice into 6–8 wedges, and serve with extra pesto and fresh basil.
