Less a full build, more of a spell combo I'd like to highlight:

Quote Originally Posted by Ashardalon's Stride
When you move within 5 feet of a creature or an object that isn’t being worn or carried, it takes 1d6 fire damage from your trail of heat.
Quote Originally Posted by Find Steed
While mounted on your steed, you can make any spell you cast that targets only you also target your steed.
It sure is a shame those two things don't appear on the same spell list, right?

Enter:
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The Lorerunner

This character was likely some sort of courier who learned secrets and stories from across the land in the course of their deliveries.

Class: Lore Bard 6, into full caster levels of choice after*
Race: Tons of good choices here, but my first instinct is High Elf to get Booming Blade, which will serve you well later. You can also grab it with something like a Sorcerer dip or Magic Initiate if you prefer something else.
Equipment and stats aren't super important here. If you have a neat multiclass idea, make sure you have the stats for it, but otherwise just max CON and CHA like any typical CHA caster.
Useful feats: Metamagic Adept. Transmuted Spell will help you circumvent fire-resistant enemies with your combo. You'll want stuff like War Caster and Mounted Combatant to protect your combo once you get it.

Your goal from levels 1-5 is to survive and just be generally useful--nothing too unusual to note here. At level 6, you'll use your Additional Magical Secrets to pick up Ashardalon's Stride and Find Steed. At level 7, you can start upcasting Ashardalon's Stride to multiply the damage the combo does.

Warhorse has a speed of 60 feet. Ashardalon's Stride bumps that to 80. Cast it on you and your steed as a bonus action, dodge or Booming Blade with your action depending on how much danger you find yourself in. Deal 2d6=7 damage to basically every nearby target. Double that when you hit 7. Set things on fire. Sow chaos. Cackle maniacally.

In single target fights, you won't get as much mileage out of Ashardalon's Stride, but Bards do get the new Kinetic Jaunt spell from Strixhaven (DM permitting, of course), so if you took that you can save your higher level spell slots and do sort of the same thing, diving in and out with Booming Blade.

*There is one other fun interaction with the Ashardalon's Stride spell I've recently been made aware of: like Sneak Attack, you can proc the damage offturn if you find a way to move with your reaction. Scout Rogue is the only way I'm familiar with, but if there are any others, let me know! Personally I think delaying full casting levels doesn't justify it offensively until relatively late, but it could be a good escape option nevertheless.