Tip the anchovies into a sieve and shake out the broken bits and powder at the bottom, which scorch and taste bitter.
Dry-toast the anchovies alone in a bare pan over medium heat for 2 to 3 minutes, stirring, until they smell nutty and rattle stiffly against the pan. Tip them onto a plate.
In a small bowl, stir together the soy sauce, rice syrup, mirim, sugar, and gochugaru until the sugar dissolves. Mix this completely before it goes anywhere near the pan.
Wipe the pan, add the neutral oil and garlic, and cook over low heat for 20 to 30 seconds until the garlic smells sweet but has not colored.
Take the pan off the heat, or turn it to the lowest setting, and pour in the premixed sauce. Swirl for 10 to 15 seconds until it loosens and bubbles at the edges.
Return the anchovies and toss fast and evenly for 30 to 40 seconds, no longer. Every piece should be coated and still rigid.
Off the heat, add the sesame oil, sesame seeds, and nuts or chili slivers, and toss twice more.
Immediately spread the anchovies in a thin single layer on a plate or tray and leave them uncovered until fully cool. Do not leave them piled in the hot pan.