Parametrized Egg

\documentclass[tikz,border=10pt]{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{colormaps}
\begin{document}
\begin{tikzpicture}
\begin{axis}[colormap = {egg}{
        color(0cm)  = (brown);       color(4cm)  = (brown!80);
        color(8cm)  = (brown!60); color(12cm) = (brown!40); 
        color(16cm) = (brown!20);        color(20cm) = (brown!10)},
    hide axis, clip=false,
    y domain=0:2*pi,
    samples=50,axis equal, view={45}{20}]

\addplot3 [domain=-1:1,surf,z buffer=sort, draw=black!50!brown, join=round] 
    ({sqrt(1-x^2)*cos(deg(y))},
     {sqrt(1-x^2)*sin(deg(y))},
     {sqrt(x+2.2)*x});

\end{axis}
\end{tikzpicture}
\end{document}