Verify my lasagne

Retina, 38 34 bytes

Thanks to Grimy for saving 4 bytes.

Have a regex with your lasagne.

Byte count assumes ISO 8859-1 encoding.

^([, ]+¶)?,{5,}(¶[@#]+¶[-~]*){2,}$

Assumes that the input ends with a trailing linefeed. Prints 1 (match) for valid lasagnes and 0 (no match) for invalid ones.

Try it online!

Explanation

This is just a standard .NET regex matched against the input, except that Retina provides the alias ¶ for linefeeds or \n.

Since the input is guaranteed to be rectangular, we only need to check the width of the lasagne on one of the rows.

^           # Anchor the regex to the beginning of the input.
([, ]+¶)?   # Match an optional first line of only commas an spaces.
,{5,}       # Match at least 5 commas.
(           # Match this at least twice to ensure at least two layers of sauce.
  ¶[@#]+    #   Match a line of sauce.
  ¶[-~]*    #   Match a line of pasta. This line may be empty (which would
            #   indicate the end of the input.
){2,}
$           # Make sure we've indeed reached the end. Note that `$` can
            # match either at the very end of the input, or in front of
            # the trailing linefeed.

Grime, 43 bytes

e`[ \,]+/?/(\,/[#@]^/[\-~]/+/[#@]/?)+{5-,4-

Try it online! Prints 1 for match and 0 for no match.

Explanation

Grime is designed for matching two-dimensional patterns, which are constructed piece by piece from smaller patterns. I define the optional top layer first, then the other layers by repeating a vertical stripe.

e`                                           Match entire input against pattern:
        /?                                   Optionally
  [ \,]+                                     a row of spaces and commas,
          /                                  below that
           (                       )         this pattern
                                    +        repeated horizontally
                                     {5-,4-  having size at least 5x4. 
                                             The brace is closed implicitly.
                                             "This pattern" is a vertical stripe containing
            \,                               a comma,
              /                              below that
               [#@]^/[\-~]                   a sauce character on top of a noodle character
                                             (the ^/ is like / but with higher precedence)
                          /+                 repeated vertically,
                            /                below that
                                 /?          optionally
                             [#@]            a sauce character.