A solution using tcolorbox; page breaks are allowed:
\documentclass{article}
\usepackage{tcolorbox}
\tcbuselibrary{most}
\usetikzlibrary{calc}
\usepackage{lipsum}
\definecolor{myblue}{RGB}{112,146,190}
\newlength\myleni
\newlength\mylenii
\newlength\quotewidth
\setlength\myleni{20pt}
\setlength\mylenii{40pt}
\newtcolorbox{mybox}{
breakable,
freelance,
remember,
colback=white,
center upper,
coltext=myblue,
left=1.5cm,
right=1.5cm,
top=0pt,
bottom=0pt,
fontupper=\itshape,
frame code={%
\fill[myblue] let
\p1= (interior.north),
\p2= (interior.south) in
(current page.west|-interior.north west) --
([xshift=-\myleni]interior.north west) --
([xshift=-\mylenii]interior.north west|-( 0,0.5*\y2+0.5*\y1 ) --
([xshift=-\myleni]interior.south west) --
(current page.west|-interior.south west);
\fill[myblue] let
\p1= (interior.north),
\p2= (interior.south) in
(current page.east|-interior.north east) --
([xshift=\myleni]interior.north east) --
([xshift=\mylenii]interior.north east|-( 0,0.5*\y2+0.5*\y1 ) --
([xshift=\myleni]interior.south east) --
(current page.east|-interior.south east);
}
}
\begin{document}
\lipsum[4]
\begin{mybox}
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Suspendisse elementum luctus odio sit amet mollis.
\end{mybox}
\lipsum[4]
\end{document}
