Knowing the name of such a texture is half the battle. This is technically "noise".
According to the documentation, Paint.NET comes with a standard Generate Noise menu option. To create this kind of texture, start with a blank beige background and then use Add Noise to make it look grainy.
The documentation does not say if there is a dialog or interactivity of any kind involved. If not (and then it lags behind software such as Photoshop), you may be able to enhance or suppress the actual average color by playing with changing the overall Brightness. You can also experiment with creating a noisy image at twice the required size and then downsize it.
I did not search [*] but I'm sure there is dedicated noisy image generator software to be found on the web.
[*] I'd write my own, probably based on the standard
random() function available in many programming languages. If that's no good I'd look in on actual noise algorithms; Perlin noise, for example.[**]
[**] More likely actually, I'd probably use Photoshop.