Step 1

Cook pasta in a large pot of boiling salted water, stirring occasionally, until al dente. Drain, reserving 2 cups pasta cooking liquid.

Step 2

Toast black pepper and 2 Tbsp. pink pepper in a dry large skillet over medium, shaking often, until fragrant, about 30 seconds. Add 3 Tbsp. butter; cook, swirling pan, until butter foams, then begins to brown, about 2 minutes. Stir in 4 oz. Pecorino and 1 cup pasta cooking liquid until combined. Add pasta, dates, and ½ cup pasta cooking liquid; cook, tossing often and adding more cooking liquid if needed, until sauce is glossy and coats pasta, about 2 minutes. Add lemon juice and remaining 1 Tbsp. butter; toss to combine.

Step 3

Divide pasta among plates or shallow bowls and top with lemon zest, more Pecorino, and remaining 1 Tbsp. pink pepper. Season with sea salt.