There are HQ stats though, in the form of stat caps. For example:
Black Truffle Risotto
Determination +3% (Max 14)
Vitality +2% (Max 15)
Crit Hit Rate +2% (Max 9)
Black Truffle Risotto (HQ)
Determination +4% (Max 17)
Vitality +3% (Max 19)
Crit Hit Rate +2% (Max 11)
The thing to ask for would be 30min duration staying even with death (even if only for One/Two Star foods)