Cut the block of tofu into smaller slabs. I usually cut the thickness into thirds and then cut the slices into quarters, to make 12 pieces. Place the pieces on a paper towel lined cutting board, place more paper towel on top. Place another cutting board, or another flat item (baking sheet?) and weight it with a can or pan or something to help drain the tofu. You don't want it to be TOO heavy, or the tofu will crumble. I sometimes slightly tilt it towards my sink so the extra water will drain. Otherwise, you may want to replace the paper towels with fresh ones half way through. Drain/press for 10-20 minutes.
Meanwhile, prepare the sauce. Combine the soy sauce, mirin, sake, water, sugar, and butter in a small mixing bowl. You don't need to melt the butter. Grate or mince the garlic and add it to the mix. Set aside.
Lay the tofu pieces out and dust one side with potato/corn starch. Flip the pieces and dust the other side.
Heat some oil over medium heat in a nonstick pan. You can choose how much you want to use here. Use just enough to cover the bottom to keep it lighter, or put more in for a more "fried" texture. I personally like to put about a centimeter's worth in. Place the tofu into the pan and cook until golden brown. Flip the tofu and cook the other side until golden brown. Do a quick sear on the sides, if desired.
Remove the tofu and drain on a paper towel lined plate. Remove any excess oil left over in the pan, and add the sauce. Lower the heat to medium low and stir until the butter is melted. Add the tofu and push them around the pan, flipping occasionally, until the sauce is thickened and sticking to the tofu. The sauce should turn nice and shiny and glaze-y and coat the tofu. By the end, there should be very little sauce left in the pan.
Remove the tofu from the pan onto a plate and garnish with sliced green onions. Serve with rice!