Hey @boulagab ! For the solution you showed you’d just need to delete the big face underneath and then fill in the gaps including the new edge. A option would be to extrude out the curve after you convert it to a mesh and then use the Boolean modifier to slice the topology into the face.

You could also give this addon a try, which lets you manipulate edge loops as if they were curves: https://www.blendermarket.com/products/bezier-mesh-shaper
Hope that helps!