Counters are most often 36" tall by 24" deep. Cinder block or concrete blocks are 16" long by 8" wide by 8" high. If you use block as a base there will be only 8" left between the front and back wall for storage. Brick sizes vary but are most often 8" long by 4" wide by 2 1/4" high, so space between the front and back walls will be 16". That is large enough to house the 20# propane tanks intended for grills. However, propane tanks should be stored in ventilated spaces. Vertical gaps can be left between bricks, or holes drilled in access doors with screening added to openings to keep out insects.

Instead of wood, use metal studs. That will give you a thinner frame but be fireproof.

Using 4" block and brick could give you the space for propane and other storage requirements, but it seems the trend is using metal studs and cement board, allowing for all types of appliances etc. The overiding concern, I think, is the foundation. With any of these systems a proper foundation would be called for with the possible exeption of a thin brick veneer applied directly to the cement board (see C). This system may work with a good structural slab, and move with the slab during temperature changes. Otherwise a foundation to regional frost or per building code would be recommended for a longlasting project, see A & B. Also keep in mind proper moisture control, as in typical construction, as I have see a number of wet interiors on outdoor kitchen islands.

IMO it iwould proabbly be easier and not much more to get proper outdoor cabinets and configure them how you like . There are many outdoor kitchens done with wood framing and wood cabinets but you can also buy metal framing kits. I can’t tell from the picture where you are planning this , if you mean along the railing your table will have to be moved a t least 5’ further away.

One of my outdoor kitchens are 6” inch thick cement blocks with a stone veneer. However, this definitely required concrete footings to be poured.

I don't like using 4" block for an entire kitchen, as there's no way to tie everything together with rebar. 6" block works though. And many outdoor kitchens are 30" deep front to back to allow for more storage. If you look up the cabinet and drawer inserts (Fire Magic, etc) you'll be able to see what sort of clearances you need.

Don't forget the required cross ventilation.

I've only ever torn out the metal frame ones so I don't know the cost difference. DIY, block is probably cheaper, but if you're hiring it out it'll likely cost more just from a labor standpoint.

They're not cheap, but you could always consider these: http://www.eldoradostone.com/types/building-blocks/ It's a pretty smart system, they seem rock solid, and install's a snap.