I’d like a drama where FL loves to eat and drink, and is happy when doing so.

Little Forest - this is fitting this most

Dating in the kitchen - She does not per say eat all the time but she does cook very delicious food
Dinner Mate
Wok of Love - again she likes to cook, he is the foodie

I'd say 

Chef Hua (2020)

36 episodes of FL cooking (and it shows a LOT of cooking and food) and people eating whatever she cooks

  • Dine With Love- FLs a good cook who's always cooking for her coworkers, ends up having to teach her boss how to cook for a show.
  •  Delicacies Destiny +1
  • Maybe A Camellia Romance- The FL is a good baker, she makes sweet treats throughout the drama
  • Also maybe..Ga Doo Ri's Sushi Restaurant- The FL owns a restaurant. We see some scenes of her cooking, and the ML enjoying her food, but the first 3 recommended might go along with your original post question better.
  • Sweet Sweet- ML needs/wants more of the ice cream the FL makes.
  • Patisserie Mon

Let's Eat : FL & ML both love to eat. Many scenes in this will make you hungry, so always remember to grab something to eat before you watch it ^^. (Bonus: if you like the first season, there are 2 more seasons and in both FLs are big eaters.)