How to put a block in a minecart in 1.13?

In 1.13, a minecart's display block is now determined by a DisplayState compound, which looks like this:

DisplayState NBT format

Which means to summon a minecart with cake in it, you should use the following command:

/summon minecart ~ ~ ~ {CustomDisplayTile:1b,DisplayState:{Name:"cake"},DisplayOffset:1}

You can also use this to specify block-states. For example:

/summon minecart ~ ~ ~ {CustomDisplayTile:1b,DisplayState:{Name:"redstone_lamp",Properties:{lit:"true"}}}