Preheat the oven to 425°F. Place a large sheet pan in the oven while it preheats so it gets super hot. Bring a large pot of heavily salted water to a boil.
Slice the chicken breasts in half horizontally to create thin cutlets. Place them between two pieces of plastic wrap and pound them to about ½-inch thick using a meat mallet.
In one shallow bowl, whisk together the eggs, hot sauce, kosher salt, and a few cracks of black pepper. Add the seasoned panko to a second shallow bowl.
Add the chicken cutlets to the egg mixture and toss to coat. Working one at a time, let the excess egg drip off before pressing each cutlet firmly into the panko until fully coated on both sides.
Carefully remove the hot sheet pan from the oven and line it with parchment paper. Drizzle the parchment generously with olive oil. Place the breaded chicken cutlets on top, then drizzle the tops with even more olive oil.
Bake for 10 minutes. Flip the chicken, drizzle with a little more olive oil, then bake for another 10–12 minutes, or until the chicken is golden brown and crispy and the internal temperature reaches 165°F.
While the chicken bakes, cook the rigatoni according to the package instructions until al dente. Reserve at least 1 cup of pasta water before draining.
Add the butter to a large skillet over medium heat. Once melted, stir in 1 tub of Castello Whipped Dip with Cracked Pepper along with ¼ cup of pasta water. Whisk until smooth and creamy.
Add the drained pasta and toss until fully coated. Add more pasta water, a little at a time, until the sauce becomes glossy and silky.
Divide the pasta between bowls and top each with a crispy chicken cutlet. Add a dollop of the remaining Castello whipped dip on top for extra creamy, peppery goodness.
Finish with flaky salt, fresh cracked black pepper, and a drizzle of olive oil before serving.