I don’t know that I would call that a “menu” necessarily, because “menu” has some rather different and specific UI semantics, but it should be pretty straightforward to build that yourself. Personally, I would use the standard CSS grid layout, but you could use Ionic’s grid if you prefer. As for icons, I’m a big fan of Font Awesome, but again Ionic has a set too.
So instead of thinking of it as a menu, I would work on building a bunch of buttons that are laid out in a grid. As buttons, they can do whatever you want when clicked. Further detail would depend on which Ionic version you are targeting, because navigation is pretty drastically different between v3 and v4.
Thanks Rapropos. Great advice and links!