Doors – Does the rough opening for this door need to be reframed

From you description, it sounds like you have a hair over 1 1/2 inches of extra space to make up. If this is correct consider this method. Place a full 1x4 (or whatever the depth of the wall may be) on both sides, as long as the new door frame will still fit comfortably in the new opening. When ever possible, I like to mount the hinge side to a solid petition without excessive shims. This makes it more solid without having to bridge a large gap with your finish nails, and makes it a lot easier to perfectly plumb the hinge jam. I often replace the center hinge screw on the jam side with a longer matching screw that will attach to the jam. This does a few things for you. One, you don't need as many nails, gives a much more solid feeling and sounding door, and gives you a tool to fine adjust the plumb if necessary.(especially on heavier solid wood doors. Just like with security screws on an entry door. After you are sure you are happy with the plumb on the hinge side, simply use visual to get an even gap on the top and latch side, in that order. You can then use shims on the latch side and shoot your finish nail just below your shims. this keeps the shims from dropping as you work down the jam. i don't usually shoot through the shims because they often split and I may want to slightly adjust them before the trim casings are installed.

Your idea about the 1X6 on either side is a good start. It would give you something to fasten to, in a simple fashion on both sides, although the fastening would be minimal. You may need to increase the number of nails in the jamb to keep it in place over the long haul. Same thing if you use screws.

When the 1x6, for a 6" wall, or if it fits, 1X8 for an 8" wall, is set in place, use construction adhesive between the block and 1X and let it harden. Make sure your block are clean so the glue sticks. This will give a firm base to work to. Do not skimp on the glue. Use a 10 oz tube, a half tube at least, on each side before you set the 1X. Use concrete screws to fasten it in place, they are more reliable for a first time installer. You could use masonry nails but there are places they may not hold. The screws may fail in their holding, but that will be obvious. To increase the chances of holding, use the screws only in the block, not the joints. Keep the screws about an 1 1/4" to 1 1/2 from the edges of the block. The block is thicker there and is far enough from the edge to keep from cracking out (should be). Screws also only affect a small area when they fail, nails break out larger pieces.

To answer the other part of your question, yes you could use framing only on one side, them shimming and fastening the other side is tricky. There are case hardened finish nails to do this, or even screws. For a first timer, what I mention above should do what you need.