Eh, the original post wanted a convex disk that would have a uniform gravitational pull, flatness was already thrown out as a design requirement. Once convex disks are allowed, a specific category of convex disk that provides a uniform perpendicular gravitational field comes to mind. The sphere. The very object we were trying to avoid. It is one of those it's funny because of the irony things.
The post clearly described a non-convex shape, and "flat-surfaced shape" should be a pretty clear instruction as well. The shape described may be visualized as a cylinder with a cone cut out, where the base of the cone aligns with one of the bases of the cylinder, and its tip with the center point of the other cylinder base. Except that the cylinder may be modified so that, seen in a cross-section, the line going from the base to the tip on either side may be a (convex or concave) curve. It makes sense as a starting point in the search for a shape with the desired properties. And it can immediately be seen to be non-convex in both described configurations, given that there's a cavity cut out.
You misunderstood, I mean for the top to be flat but the "underground" to have some kind of shape to compensate for the gravitational pull at all points on the flat surface. For a 2Dish example in the ballpark, you could think of one of these wooden toy bridge blocks: https://thumbs.dreamstime.com/b/natural-wood-blocks-364582.j...
I think you could construct a curve such that the mass's gravitational pull on the right cancels out the pull on the left, for any point on the surface.
