How can I get double angle brackets, i.e. - << >>

The following works for me:

Expression\(\langle\)Func\(\langle\)T, bool\(\rangle\rangle\)

(\(…\) is the same as $…$ but the latter is deprecated in LaTeX.)

Notice that you probably want to define macros for this to make it more readable:

\newcommand*\template[1]{\(\langle\)#1\(\rangle\)}
…
Expression\template{Func\template{T, bool}}