Preheat oven to 400 degrees and line a baking sheet with parchment paper. In a small mixing bowl, whisk together the smoked paprika, dried garlic, ground mustard, 1/2 tsp chopped fennel seeds, and 1/2 tsp black pepper.
Place the carrot coins onto the prepared baking sheet and toss with 1 Tbsp olive oil to coat. Add spices and toss until all the carrot coins are evenly coated. Spread carrots into an even layer on the baking sheet.
Roast on the middle rack for 15 minutes, flipping after 10, or until the coins are easily pierced with a fork (watch them closely as they may cook faster or a little longer depending on how thick you chopped them).
While those roast, in a small bowl, whisk together ¼ cup red wine vinegar, ¼ cup water, and salt. Add thinly sliced onions and set aside to pickle while preparing the rest of the salad.
In a small bowl, whisk together fennel seeds, orange juice, zest, vinegar, salt, and pepper. While whisking, slowly pour olive oil into the dressing until it’s emulsified. Set aside.
Drain the red onions and toss in a large serving bowl with the iceberg lettuce, carrot coins, olives, banana peppers, artichoke hearts, cherry tomatoes, roasted red pepper, and dressing. Sprinkle with feta and serve right away.