Seems to: 1. move up a text block ({) 2. enter insert mode on line above cursor (O) 3. enter a LaTeX string (\begin{quote}) 4. exit insert mode, move down a block of text (<ESC>}) 5. enter insert mode one line below the cursor and enter the closing LaTeX string (\end{quote}) 6. exit insert mode and move back up to the start of the text block, enter visual mode, move back to the bottom of the text block and also selecting it (<ESC>{v}) 7. while still in visual mode run a normal mode command that moves to the end of the line and inserts "\\" at the end of the line.

So the output would be

\begin{quote} \\

\end{quote} \\