Drain the tofu. Wrap each block in a clean kitchen towel, set a heavy pan on top, and press for 20 minutes. The towel should be damp and the block should feel noticeably firmer.
Cut each block lengthwise into 4 slabs about 3/4 inch (2cm) thick. Pat each slab dry.
Whisk the stock, soy sauce, rice vinegar, and honey in the slow cooker insert. Add the garlic, ginger, and scallion whites.
Lay the tofu slabs in a single layer, slightly overlapping if needed. The liquid should come about halfway up the sides. Cover and cook on LOW for 2 hours, until the slabs are hot, a little darker on the surface, and smell savory and gingery. Check at 90 minutes, and do not stir.
Heat the broiler to high with a rack 15cm (6 inches) from the element. Line a rimmed baking sheet with parchment.
Lift the tofu out with a wide spatula, supporting each slab from below, and set it on the baking sheet. Strain 1/4 cup (60ml) of the braising liquid into a bowl.
Melt 2 tablespoons of the butter in a skillet over medium heat. Add the anchovies, garlic, and chili flakes and stir for 1 to 2 minutes, until the anchovies dissolve into the butter and the garlic smells fragrant but is not browned.
Pour in the strained liquid and the honey. Simmer for 3 to 4 minutes, until reduced by about half and glossy. Take the pan off the heat and swirl in the remaining 2 tablespoons butter, lemon zest, and lemon juice until smooth.
Brush the glaze over the tops of the tofu. Broil for 3 to 4 minutes, until the glaze bubbles and the edges turn golden brown. Watch closely, since the honey can burn. Scatter parsley over the top and serve.