Help with blender bevel

I’m trying to model a waterpollo ear protector in blender. I’ve made the base by scaning it ant extruding from a vertex and now I have the basic shape.
I want to make it round, so I extrude it, rotate a bit the top part on the x axis and fill the face. Alt-select the border and bevel it, but I can’t go untin it is completely rounded, as it break.
How should I go about this? Can I make it work like this or I should take a different approach to modeling it and, in such case, do you have any idea?

I’ll add some images to represent what I say:


Welcone :tada:

… i think you would be better of by using a halfsphere and transform it with propotional editing or even a lattice… bevel would only “smooth” the edge… but you dont want one smoothed edge you want a curved edge…

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Maybe even start with a halfed 45deg roated subdivided cube:


Oh, wow, that is pretty close and would just need a few modifications, thanks.
How did you achieve that? I’m not able to figure out. I’ve tried adding a subdivision surface to a cube after subdividing it in edit mode, but it just works with 1 subdivision, with more it doesn’t round it at all, as the edge is smaller. Could you provide some instructions for me to replicate what you did on the image?

Thank you very much

A cube 3 times subdiv, all faces individual inset…

…then grab some points at the front side and proportional edit…