What is the space next to it that looks like a door or shelves?

If you provide us with a floor plan with measurements of this whole spot, we might be able to help you.

I would remove the stud and make the wall flush to allow for shelves to fill the space.

Could that be storage for your broom, vacuum, mop, etc. with one high shelf for bulky items like extra paper towels?

I think it will look odd to have it be open shelving. I would put a door on and use it for items such as what J from Lakes Country suggested, or you can put small appliances and other items on shelves. If you are worried about shelves being too deep, the shelves need not be full depth and could have some wasted space at the front of the closet to keep things from getting lost in the depth of the closet, where it is hard to reach. You could hang things on hooks in the wasted wall space at the front of the closet if you want. I have a pantry closet that is similarly sized--I'm not keeping canned items or anything like that in it. My shelves are 26" deep X 24" width. I hang things on the wall (immersion blender in the bag to the right) towards the front of the closet.

broom closet is a good idea

Here is concept. Put two long shelves stained or painted wood that run across that space and into the closet. For frequently used items. Then in lower area you could do a deep drawer that could hold larger items or whatever you need easy access to. Or if you have kitty or doggie you could carve an entry into the drawer that kitty could get into or hold a litter box.

Brooms and mops would love it here. Can a door be made to cover the open space?

What is on the other sides of it? Can’t be incorporated to those spaces?

What storage needs remain after the remodel?

Wall system for sure. doesnt have to be any more complicated…keep options for a variety of things stored there… and not expensive..seems to be different types of systems.

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Not an expert. But then you’ve given us no measurements, so you’re a little light on info for experts to weigh in. Please read the New to Kitchens thread and provide a drawing of the space, including adjacent rooms, with measurements.

Not only is that space not big enough to walk in, its presence is keeping you from using the entire corner for cabinetry.

First I’d want to know if you could close off that corner and use the found space for whatever lies on the other side of the wall behind your kitchen.

Then I’d want to know whether the space at the right of the opening (big red asterisk) - is part of that closet as well?