Slice Brussels sprouts by holding onto the stem of each and chopping into roughly 1/4-inch rings crosswise, starting from their tops. Discard the knobbly stem pieces you’re left with. (The slices will break apart into a chaotic pile of shavings—totally fine, and no need to be overly precise with this step.) Set aside about 1 cup of the resulting Brussels sprouts “confetti.” (Note: if you prefer, you can do this step on a mandoline.)
In a large sauté pan, heat 1 tablespoon oil. Add the non-reserved Brussels sprouts with 1 teaspoon kosher salt. Sauté over a medium-high flame about 2 minutes, until just wilted and vivid green. Transfer to a large bowl and add the olives, artichoke hearts, peppers, and cheese. Toss together—the cheese will mostly melt.
In another bowl, whisk together remaining 3 tablespoons oil with the vinegar and lemon juice, plus a big pinch of salt. Pour dressing over salad and toss again, adding the reserved raw Brussels sprout shavings. Taste and adjust seasoning as needed with more salt and lemon juice, to make the flavors pop. Serve individual portions topped with toasted breadcrumbs and more cheese.
Ella Quittner is a contributing writer and the Absolute Best Tests columnist at Food52. She covers food, travel, wellness, lifestyle, home, novelty snacks, and internet-famous sandwiches. You can follow her on Instagram @equittner, or Twitter at @ellaquittner. She also develops recipes for Food52, and has a soft spot for all pasta, anything spicy, and salty chocolate things.