**Do ahead:** Dressing can be made 3 days ahead. Cover and chill.
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#### Step 1
Bring 1 cup water to a boil in a small saucepan. Remove from heat and immediately add bulgur. Cover pan and let sit until bulgur is tender, about 10 minutes. Drain off excess water, then mix in dill and 2 Tbsp. oil. Season with salt and pepper.
 
#### Step 2
Meanwhile, whisk shallot, vinegar, sour cream, mustard, and ¼ cup oil in a small bowl until smooth; season dressing with salt. Set aside.
 
#### Step 3
Heat remaining 1 Tbsp. oil in a large nonstick skillet over medium-high. Season salmon with salt and arrange skin side down in skillet. Reduce heat to medium and cook, pressing down gently on fish, until skin is golden brown and crisp, 6–8 minutes. Turn fillets over and cook until just cooked through, about 3 minutes. Transfer to a large plate, arranging skin side up.
 
#### Step 4
Combine fennel and radishes in a large bowl. Drizzle reserved dressing over to suit your taste (you won’t need all of it) and toss to coat. Season with more salt if needed.
 
#### Step 5
To serve, spoon bulgur among plates, dividing evenly, and top each with a salmon fillet and fennel and radish salad.