Time with former lovers consuming Frenchman’s cuisine (3-3)
I believe the answer is:
Here is my best explanation:
'cuisine' is the definition.
'time with former lovers consuming frenchman's' is the subsidiary indication.
'time' becomes 't'.
'with' says to put letters next to each other.
'former lovers' becomes 'exex' (former lover is an ex).
'consuming' indicates putting letters inside.
'frenchman' becomes 'm' (abbreviation for Monsieur - like 'Mr').
'exex' going around 'm' is 'exmex'.
(Other definitions for tex-mex that I've seen before include "Cuisine of southern North America", "Style of food", "N. American cuisine" and "North-American cuisine".)