1/4 cup inely chopped fresh flat-leaf parsley, plus more for garnish
4 ounces Parmigiano-Reggiano cheese, finely grated with a Microplane grater (about 2 1/2 cups), divided
3/4 cup (6 ounces) cold unsalted butter, cubed
Flaky salt
Direction
Bring a large pot of salted water to a boil over high. Add pasta, and cook according to package directions to just barely al dente. Using tongs, transfer pasta to a colander, and drain, reserving 3 1/2 cups pasta cooking water. Return pasta to warm pot; drizzle with 1 tablespoon of the oil, and gently stir with tongs to coat. Set aside.
While pasta cooks, heat remaining 3 tablespoons oil in a large skillet over medium until glossy and lighter in color. Add garlic; cook, stirring constantly, until fragrant and golden brown, 20 to 30 seconds. Add panko; cook, stirring constantly, until golden brown, 2 to 3 minutes. Transfer to a heatproof bowl; add kosher salt, and stir to combine. Let cool to room temperature, about 5 minutes. Wipe skillet clean. Add parsley and 1/4 cup of the cheese to panko mixture; stir to combine, and set aside.
Add 3 cups of the reserved cooking water to cleaned large skillet; bring to a boil over medium-high. Reduce heat to medium-low. Gradually add butter to skillet, whisking constantly and letting each butter cube melt before the next addition, until butter has emulsified into liquid, 10 to 12 minutes. (Mixture should be at least 180°F, uniformly creamy in color, and starting to bubble if left undisturbed.)
Add pasta to butter sauce in skillet; toss to evenly coat. Cook over medium, stirring constantly, until sauce comes to a boil (you will see bubbles in liquid in center of skillet), 3 to 5 minutes. . Sprinkle with 1 cup of the cheese; toss and stir to evenly coat pasta in cheese and sauce. Add remaining 1 1/4 cups cheese, and cook, tossing and stirring constantly, until pasta is evenly coated in sauce, about 2 minutes. If more liquid is needed for sauce, gradually add additional reserved cooking water 2 tablespoons at a time, stirring and tossing to coat. Remove from heat. Season to taste with kosher salt.
Divide pasta evenly among plates. Top each with 1 tablespoon toasted panko mixture. Garnish with flaky salt and additional parsley. Serve immediately.