Shale is not a good building material, it’s too friable (crumbly). Slate starts off as the same rock ans shale except it undergoes a bunch of heat and pressure which makes it much less friable and an excellent material for things like roofing tiles and mantles.
A lot of heat and a lot of pressure would be a start, but then there’s a time factor as well. The heat and pressure mess around with the rocks mineral constituents, but the real “magic” begins as those minerals start recrystallizing. In time (geologic time) that recrystallization makes a much harder rock.
I honestly don’t know if the process can be sped up. I’m thinking of something like firing bricks, but bricks are made with specific ingredients and certain impurities are specifically excluded because they hurt the manufacturing. When you start with shale, lord knows what mother nature threw into that specific specimen and how she arranged it.
I guess the easiest way to get shale harder might be to crush it finely, mix it with water and bake it. If you’re lucky the clay minerals will find each other and form a strong matrix. It wouldn’t be slate, or even a rock anymore, but bricks are handy sometimes.