Step 1

Heat 2 Tbsp. extra-virgin olive oil in a large skillet, preferably cast iron, over medium. Add 1–2 tsp. Calabrian chile paste, depending on your heat preference, and stir into oil. Add 1 cup panko and ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt (and ½ tsp. crushed red pepper flakes, if using instead) and cook, stirring often, until breadcrumbs are deep golden brown, 5–8 minutes. Transfer spicy breadcrumbs to a small bowl; set aside.Do ahead: Breadcrumbs can be made 3 days ahead. Store airtight at room temperature.

Step 2

Whisk 4 garlic cloves, finely grated, ⅓ cup extra-virgin olive oil, ¼ cup fresh lemon juice, 1 Tbsp. anchovy paste or about 5 drained oil-packed anchovy fillets, smashed, 1 Tbsp. Dijon mustard, and ¾ tsp. Diamond Crystal or ½ tsp. Morton kosher salt in a large bowl to combine. Add 3 English hothouse cucumbers, cut on a diagonal into 1" pieces, to dressing; toss well to coat. Add 4 oz. Parmesan, shaved, and 1 cup coarsely chopped dill; gently toss to distribute evenly. Taste and season salad with more salt if needed.

Step 3

Just before serving, transfer cucumber salad to a platter and spoon reserved spicy breadcrumbs on top.Do ahead: Dressing can be made 3 days ahead; cover and chill. Salad (without breadcrumbs) can be made 3 hours ahead; cover and chill.