1to1 play your class [ EDIT ]

We have all played in a game where the core of your character has been sidelined due to the overarching plot. The druid who's swor to protect the valley is now plane-jumping around hunting down a power crystal for a magical wand. Or the righteous paladin, making deals with the thieves guild. Or the cleric, whose god becomes a sidenote. This is exactly what I don't want to do.

My idea is to play a one-on-one game, where we follow one character, who gets their class, advances through it and what happens during that time.
How did the character become a warlock?
What happened when the sorcerer gained mastery of new 2nd-level spells?
Why did goblins become the Rangers favorite foe?
How did the tiefling become a master of the elven magic tradition of Bladesinging?
Questions like these are what I would like to explore.

So I suggest the following:
Frequency: 1 post per day
System: A class system like D&D 5e
Setting: Whatever we like.
Duration: As long as we are both having fun
Both of us will be GM'ing for each other's characters
We will frequently discuss the story direction, and what kinds of challenges, setbacks or scenes we would like to have with the character. I have zero plot ideas right now. The story is centred around the character.