We miss the days when everything had daughterboards. Now, Arduinos have shields and Raspberry Pis have hats. The BeagleBone has capes. Whatever. However, regardless of the name, the open source BeagleWire cape/shield/hat/daughterboard connects to a BeagleBone and provides a Lattice iCE40HX FPGA, some support hardware, and common I/O connectors like Pmod and Grove. You can see a video about the board below.
In addition to the FPGA, the board contains a EEPROM, RAM, flash memory, an oscillator, and a few buttons, switches and LEDs. The buttons even feature hardware debouncing. The parts list and design files are all available and — depending on a successful crowdfunding campaign — you might be able to buy one for $75 in the future.
The board is configured to communicate over the 100 MHz 16-bit GPMC port. Linux software and example drivers are available so it should be fairly simple to get the FPGA and CPU talking to each other for your own purposes.
If you decide to build your own, there’s a one-click button that will populate a DigiKey cart for you with most of the components. Although the DigiKey site complained about an error, it did seem to order 24 of the 26 components and the total came to just over $50. Of course, you’d still need to source the missing parts and the board.