Heat oven to 425F. Chop broccoli into very small pieces. Place on parchment lined baking sheet. Add shredded Brussel sprouts to sheet. Drizzle with olive oil and salt, toss, and bake for 20 minutes, tossing half way through. Let cool.
While baking, chop pitted medjool dates and salted almonds into small pieces. Set aside.
Cook raw, peeled, tail off shrimp by heating a pan over medium heat. Add butter and Calabrian chili paste. Add shrimp and a pinch of salt. Cook two minutes per side and turn off heat. Set aside.
Make dressing by whisking together olive oil, Calabrian chili paste, lemon zest, lemon juice, honey, and salt. Set aside.
Assemble salad by putting roasted veggies in bowls, then add cooked shrimp, dates, almonds, and grate fresh pecorino Romano on top.
Drizzle dressing evenly over salads. Enjoy!