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1
Place half of the butter in a medium bowl and mash with a spatula until spreadable.
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2
Add the mustard, season with salt, and stir to combine.
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3
Place the mustard butter on a sheet of plastic wrap.
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4
Roll into a log and twist the ends to seal.
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5
Place in the refrigerator to harden, at least 30 minutes.
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6
Meanwhile, make the fish.
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7
Place the paprika, cayenne, measured salt, thyme, black pepper, and sugar in a small bowl and stir to evenly combine; set aside.
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8
Melt the remaining half of the butter and place it in a small bowl.
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9
Liberally brush one side of each catfish fillet with butter, evenly sprinkle the buttered sides with half of the spice rub, and press gently on the fillets so that the spice rub adheres.
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10
Flip the fillets, liberally brush with butter, evenly sprinkle with the remaining half of the spice rub, and press gently so that the spice rub adheres.
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11
Heat a grill pan or outdoor grill to medium high (about 375 degrees F to 425 degrees F).
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12
When the grill is ready, rub the grates with a towel dipped in vegetable oil.
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13
Place the fillets on the grill and cook undisturbed until grill marks appear and the fish is opaque, about 3 to 4 minutes.
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14
Using a flat spatula, flip and cook until completely cooked through, about 3 to 4 minutes more.
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15
Transfer to serving plates.
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16
To serve, cut 4 (1/4- to 1/2-inch-thick) rounds of the mustard butter (you will have some left over, but can serve more slices if desired).
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17
Place a round on top of each piece of fish and serve immediately with the lemon wedges.
