I actually did this with DD1, who was subletting a room one summer.
I taught her to make:
An omelette, fried egg, scrambled egg, boiled egg and hard boiled egg;
How to make a simple tomato sauce from scratch using tinned tomatoes, garlic, basil, s&p, maybe a little wine;
To boil pasta as dente and cook rice without burning;
Bechamel sauce;
Simple spag bol including carrots, onions, celery, simple tomato sauce, dash of wine, mince;
-- how to use basic spag bol and make lasagne or shepherds' pie for the next days;
Simple cream, stock and wine sauce with herbs, etc;
Alfredo sauce;
A simple lemon sauce for chicken to go with rice or pasta;
A simple tuna sauce for pasta with parsley and olives that I make in summer that she liked;
A simple stir fry involving any sort of meat and various veggies to go with noodles or rice;
Simple homemade curry;
Pancakes, crepes, soda bread, simple french bread dough (yeast) and pizza dough;
How to chop up a whole chicken, debone, etc;
How to roast a chicken, test for doneness, strip meat or carve;
How to use cold, cooked chicken for a few dishes later in the week;
Chicken caesar salad;
Thai chicken salad (Nigella);
How to make basic chicken stock and freeze in usable portions of about one cup;
Pan gravy using chicken or beef juices;
How to bread chicken and pork;
How to cook veggies and not end up with a soggy unappetising mess;
How to peel and boil potatoes;
How to mash potatoes properly;
Salade nicoise;
Panzanella salad (to use up bread basically);
Green split pea soup;
Minestrone soup;
Pasta e fagioli soup/stew (she loved this at home).
Shortcrust pastry (good for sweet and savoury pies alike);
How to use phylo pastry;
A few pie fillings;
Victoria sponge;
Brownies.
How to read a recipe right through before getting started, and how to figure out order of operations - turn on oven first, butter pans, etc.
I also taught her food hygiene and basic kitchen safety, especially about meat safety, hand washing, using sharp knives always. Also, how to buy bulk sized packages, split them up into portion sized pieces, and wrap, mark and freeze each item. How to thaw meat safely and the need to plan ahead to give enough time for thawing. And how to clean up.
I gave her a present of a small cast iron pan and a pair of cake pans, a few wooden spoons and a nice whisk, and let her at it. She had a little dinner party for her friends with an apple pie for dessert two weeks later.