In some cases, I list multiple recipes of the same dish that are intended to be of easier difficulty at first and tougher as you go down the list. This and cooking is intended to be for fun as is the show so have at it!
Captain Pike's Apron
All cotton apron
https://www.simons.ca/en/kitchen-dining/aprons-oven-mitts/charcoal-canvas-apron--12263-1152120
Season 1, Episode 1 - Strange New Worlds
Captain Pike cooks pancakes and serves it with a strawberry sauce and butter. Also on the table is Coffee and Orange.
Links to buttermilk pancake recipes:
https://bakingmischief.com/make-fluffy-buttermilk-pancakes-two/
https://cooking.nytimes.com/recipes/1893-everyday-pancakes
Links to strawberry sauce recipes:
https://bakingmischief.com/strawberry-sauce-for-pancakes/
https://cooking.nytimes.com/recipes/6096-strawberry-sauce
https://damndelicious.net/2012/07/23/buttermilk-pancakes-with-strawberry-sauce/
Season 1, Episode 2 - Children of the Comet
In the second episode of the first season, the cadet class is invited to the Captain's quarters for a dinner party. He has what appears to be very large sized ribs, a salad, shish kebab and some hors d'oeuvres. Because of the size of the ribs, I will assume it is not baby back but St. Louis style (pork) ribs but beef plate ribs. He has them grilling (not smoked) and over direct heat, other types of of beef rib would require indirect heat. Although this is what he uses, I prefer indirect or smoked ribs when possible!
It is unclear what these are and I'd take too many liberties in trying to guess. However if future episodes provide more clues, I will update this.
Season 1, Episode 6 - Lift Us Where Suffering Cannot Reach
Food was not front stage and center in this episode and it appears what they used were simple dishes.
Season 1, Episode 7 - The Serene Squall
Appears to be lasagna and salad at the dinner with Dr. Aspen. Later while held captive, Captain Pike cooks what looks like could be Chili or stew.
Season 1, Episode 9 - All Those Who Wander
Breakfast foods. In this episode the cadets are taken to a ceremonial breakfast where fruit spreads, bagels and lox and fruit and cream breakfast pastries are served. Later
Lox and Smear:
https://www.themountainkitchen.com/bagels-and-lox/
Fruit and Cream Breakfast pastries:
https://www.justataste.com/fruit-and-cream-cheese-breakfast-pastries-recipe/
Quiche Recipe:
https://www.cookingclassy.com/quiche-recipe/
Season 1, Episode 10 - A Quality of Mercy
Pasta Mama - just add eggs, parmesan lightly saute and it transforms from leftovers into something new.
He states in the show he is making Osso Busco next week I'll put a link to a recipe though it was not shown on the show, only mentioned.
Season 2, Episode 3 - Tomorrow and Tomorrow and Tomorrow
This one is interesting because La'an and Captain Kirk go back in time and are able to sample 21st century foods. This episode shows them eating hot dogs and later poutine.
Season 2, Episode 5 - Charades
Captain Pike's Cooking Lessons, always use fresh herbs, nothing synthesized. The point of whisking is to add air to increase the volume to the eggs. Vulcan specialties: Traditional Tevmel,
Easy Omelette recipe:
https://www.australianeggs.org.au/recipes-and-cooking/two-egg-omelette
Star Trek Season 2, Episode 8 - Under the Cloak of War
Jambalya with Deltan Parsley, Deviled eggs and raktajino a caffeinated drink from Kronos.
Star Trek Season 2, Episode 9 - Subspace Rhapsody
The Julia Child classic boeuf bourguignon is referenced in this episode. Foot network recipe:
https://www.food.com/recipe/boeuf-bourguignon-a-la-julia-child-148007