How can I frame-in these baskets to make it look more custom made?

Sure, use thin plywood and build a top and bottom then add the spacers with nails, glue or nail gun. Sit on top of cabinet. No need to attach if you measure the dimensions correctly. You can take the plywood top to the ceiling height and add a trim to the top that looks like built ins. (think shelving tower on it's side)

Here's an article with ideas of using the space above the kitchen cabinets. The last one deals with framing it in. I hope this helps! https://www.apartmenttherapy.com/5-things-to-do-with-that-awkward-space-above-the-cabinets-212216

go to habitat and look to see if they have cabinets that will fit the spaces .The ones that go over the fridge should be small enough .I got really nice solid oak ones cheap for my laundry room and they turned out great looking

Yes, you can add framework and cabinet doors but you'll probably have to paint all the cabinets for a uniform look. Or use a dark or chalkboard paint. If it fits your decor style, hang short curtains over that entire space, using a pipe as a curtain rod.

I really like the basket idea. Never thought of that, and the gap between my cabinets and my ceiling doesn't look great. However, I am not too keen on the baskets you have and think you could find some prettier ones with lids. The ideas about making cabinets out of plywood seem very time consuming indeed, and I am not sure how you would access to the baskets without many doors which would not only be a lot of work, but very expensive. I would stick to the idea you already have, and I shall look at my spaces now in a different light.

If I were you, I would paint the cabinets white, change the baskets, and replace the ceiling light with something more contemporary (perhaps an identical pendant lamp). But before you do anything, go through everything you have and get rid of what you don't use or don't like. Have your things multitask. A grapefruit spoon, for example, is a great strawberry huller. They sell a multipurpose pot that's a pressure cooker/crock pot, etc. in one that saves a lot of counter space.

I just happen to really like the baskets you have. But I know that whether I add cabinets or place decorative items in that dead space, I’ll never be able to use the space. It’s just too dangerous to climb a ladder to reach those areas at our ages. I love my high ceilings, but I’m still looking for smart solutions for me. 😊

It appears that you have too much stuff to store. Think its time to declutter the kitchen. Counter tops and the top of a refrigerator shouldn't be used for storage. Do you have a pantry to store excess items or a rolling cabinet/bar to use? You need to go thru these items that you have no room for and decide if you really need them.

I bought a bunch of orange colored plastic shoe boxes with matching lids (my kitchen has white uppers and orange lower cabinets). I put chalkboard labels on them and lined them up on top of my cabinets. Looks cheery and I know where everything is! The shoeboxes house my baking stuff (cookie cutters/decorating stuff/candy molds/etc.) that is only used occasionally. Good luck and have fun with your storage/decorating!

Em gives good advice. The only thing I might suggest that is different is to use MDF instead of plywood as the surfaces are usually ready to paint on MDF. I would not try to match the existing cabinetry in color but would paint the MDF the same color as the walls or the countertop.

It is hard to tell from the photo whether there are other ideas that could be offered for more storage, but I would guess you have maxed out the storage based on what I can see in the photo.