In small bowl of an electric mixer, beat butter until creamy; gradually add lemon juice, beating until mixture is fluffy. Beat in mustard, red pepper, and parsley until well blended. If made ahead, cover and refrigerate for up to 2 days; bring to room temperature before using.
Rinse salmon steaks and pat dry. Brush both sides of each steak with oil and lightly sprinkle with salt and black pepper.
Place fish on a well-greased grill 4 to 6 inches above a solid bed of hot coals. Cook, turning once with a wide metal spatula, until fish flakes when prodded in thickest part (8-10 minutes).
Using spatula, transfer steaks to a warm platter; top with butter mixture.