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1
Set the block of momen-dofu on a clean cutting board. Lay paper towels above and below it, place a second board on top, and add a moderate weight. Press for 30 minutes. The tofu is ready when the paper towels are saturated and the block has visibly compressed; if moisture remains free on the surface, press further. This step is foundational: unremoved moisture will steam the tofu on the grill rather than char it.
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2
Heat a ridged grill pan or flat griddle over high heat until the surface is very hot. Oil lightly. Place the pressed tofu block — or blocks cut to portion size — flat on the grill. Press gently but firmly so full contact is made between the tofu's surface and the grill bars or plate. Hold without moving for 3 to 4 minutes per side. This is where the dish lives or dies: insufficient heat or insufficient contact time yields a pale, steamed, softened surface; the correct result is a dark, caramelised grid of char marks on both flat faces, with a slight smoky bitterness detectable at close range.
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3
Transfer the grilled tofu to a rack and allow it to cool briefly. The exterior should feel firm and dry to the touch on the charred faces; press the side lightly — it yields less than fresh momen-dofu. The yaki-dofu is now ready to be added whole or cut into the braising vessel — sukiyaki, oden, or nimono — where it will absorb the surrounding broth over extended cooking without disintegrating.