Might I suggest
Words of Power from Pathfinder. This variant spell casting is like a more dynamic use of the Dragon Shouts from Skyrim. Spells are broken up into 3 components; Target, Effect and Meta. A player starts off knowing all the Target Words and the Boost Meta Word, though not all of them are usable at first level. Each time a player's class would gain a new spell, they chose a new Effect or Meta word less than or equal to their highest spell slot. Once a player can cast 3rd level or higher spells, they can chose to either use a single effect of that spell slot
or multiple effect from lower slots as indicated on the chart.
Having played with this spell casting variant before, I would advise the following for smooth game play and spell creation:
1- Each Word known has a note card.
2- Each card has some sort of visible indication to which component it belongs to and somewhere largely indicate minimum spell level. (I used different colored highlighters.)
3- On the card, leave space for both the variable formula(s) as well as the current result of said formula. (IE. 1d6/caster lvl | 3d6)
4- Place all the cards together on the table for the current spell being cast so they can be seen. Helps both the player to properly design the spell as well as helps you make sure there is less cheating (Either intentionally or accidentally.)
5- Play a spontaneous spell caster. The versatility of just being able to pick the Target component that bests suits the situation is where this variant spell casting shines.
6- While you can replicate a large portion of spells in the players handbook, there are spells that are too complex, niche, etc to do so. Either you & your player need to sit down and create Words fit these holes and/or allow the cast the spell as is in the source book.
After the first time I played with this system, I associated each spell Word with one of the runes from Diablo 2. So instead of saying I cast a 2nd lvl Careful [no somatic component] Burst [short range; 10ft radius] Frost Fingers [2d6 cold + 1 round staggered if save failed] I might have said Tal-Um-Mal. With the cards being used on the table for all to see and having given the DM a list indicating what rune was associated with what Word (though he just looked at the cards instead) I added a bit of role playing to my spell casting. Though the DM did rule that it was easier for those who have repeatedly heard a Word component to spellcraft the spell as a whole.