In a plate, combine flour, thyme, salt and pepper. Mix to combine.
Pour milk into a shallow bowl.
Pour eggs into a shallow bowl.
Empty bread crumbs onto a plate.
Heat enough oil for deep frying.
Dip fish first in the milk. Then place in the seasoned flour. Cover on all sides. Shake off excess and dip into the egg. Put in the breadcrumbs plate and make sure fish is coated on all sides.
Place into the hot oil and fry until golden brown on both sides, about 3-4 minutes on each side.
Remove from oil and drain on paper towels.
To make sauce, first blanche vegetables for just a few minutes until they are no longer raw, but still have a bite to them.
In a skillet, melt butter. Add flour and cook for 2-3 minutes until raw taste is cooked out of the flour. Add milk, salt and pepper. Stir constantly to avoid lumps. Bring to a boil. Simmer for 5 minutes, until sauce is thickened.
Add vegetables, lemon juice and parsley and cook another minute until vegetables are heated through.
Serve fish with sauce on top.