Season salmon fillets with 1/2 tsp. of the salt and place on a shallow plate or wide-rimmed bowl.

Prepare turmeric glaze by combining 3 Tbsp. of the orange juice, honey, turmeric, black pepper, mustard, sesame oil, and 1/4 tsp. salt in a small bowl. Spoon half of the mixture over salmon (reserve remaining) and let salmon sit at room temperature for 30 minutes.

While salmon marinates, prepare cucumber-mint salad by combining mint, cucumber, shallots, almonds, remaining 1 Tbsp. orange juice, and 1 Tbsp. olive oil in a small bowl. Set aside.

Heat remaining 1 Tbsp. olive oil in a large skillet over medium-high. Cook salmon, skin side down, undisturbed, until salmon skin is crisped and browned, 3–4 minutes. Gently turn fillets and cook until salmon is just opaque at the center, 1–2 minutes for medium rare. Transfer to a plate.

Add bulgur to skillet; cook, stirring often, until fragrant and toasted, about 1-2 minutes. Add broth and bring mixture to a boil; reduce to a simmer and cook until most liquid is absorbed, about 10-12 minutes. Stir in orange zest and remaining 1/4 tsp. salt. Nestle salmon fillets back into skillet with bulgur and spoon remaining turmeric glaze over salmon. Cook 2 additional minutes.

Remove from heat and spoon cucumber-mint salad overtop. Garnish with orange slices, if desired.