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1
Combine gochugaru, gochujang, doenjang, ganjang, and minced garlic in a bowl and stir until the paste is uniform and no dry flakes remain. Work the doenjang in thoroughly, because its dense fermented paste tends to sit in pockets and will scorch unevenly if it reaches the pan unmixed. The sauce should be thick enough to coat a spoon.
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2
Arrange the bone-in, skin-on monkfish pieces in a wide, heavy pan or braising vessel in a single layer, pour the sauce over the fish ensuring all surfaces are coated, and set over high heat. This is where the dish lives or dies: maintain fierce, continuous high heat throughout the braise so the sauce concentrates and clings rather than pooling into a thin, watery liquid that merely steams the fish. Braise for 12–15 minutes, turning the pieces once at the midpoint, until the sauce is visibly sticky and reduced, glossy and lip-coating from what the skin and bone have given it, and the fish flesh pulls away from the bone.
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3
Scatter the mung bean sprouts over and around the fish and cover the pan, keeping the same high heat, so the sprouts cook in the trapped steam rather than sinking into the sauce and turning sodden. Cook for exactly 3 minutes, then lift the lid: the sprouts should be wilted at their base but retain an audible snap when pressed between finger and thumb — their crunch is structural to the dish.
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4
Remove from heat and lay the torn perilla leaves and green onion sections over the surface, then drizzle the sesame oil across the dish so its fragrance blooms against the residual heat without cooking off entirely. Bring the cooking vessel directly to the table while the sauce is still bubbling at the edges.