Blue Adobe Slabs were introduced with Patch R36 on November 15th 2016.
2 of these slabs can be made in a Processor from one block of Blue Adobe Wall each. No crafting recipe has to be unlocked for that.
The crafting recipe for Blue Adobe Wall is unlocked by finding the rare Recipe for it in a Treasure Chest or maybe obtain it from a Thing that spawns on corrupted blocks.
8 Blue Adobe Walls each can then be crafted with 2 (blocks of) Adobe Bricks, 4 blocks of any kind of Canyonstone (like Ruddy Canyonstone, Dark Canyonstone or the rather rare caramel-colored Canyonstone), plus 2 Stone Rods made of Stone, Limestone or Bedrock in a Processor, 1x Melted Wax made of Beeswax in a Forge or found in Treasure Chests and 1 Blue Pigment made from Blue Flowers (from Elderwood trees or Wood Treasure Chests) in a Processor.
Obtaining Blue Adobe Slabs is one of the requirements necessary to unlock the crafting recipe for Blue Adobe Stairs.
Blue Adobe Slabs are also one of the requireded ingredients to craft Blue Adobe Stairs.