Not sure if these really count as David vs Goliath, but I always tend to make it as hard as possible:
Running the DTM Nordschleife race in an Opel Astra with 200kg of ballast(don't remember which way I shifted it) and a 50% restrictor, on Racing Hard tires(not sure which they use) was pretty fun. Also shows how ridiculous the AIs are at the ring. Same car, just heavier and with only half the power can still beat them, although it required utilizing the superdraft on the Döttinger Höhe to get past the last one, in fact just to avoid half the field flying past me.
My favorite offline moment was probably doing the Grand Valley 300 in my 100% showroom stock(plus only oil change that had long since lost it's bonus hp) '10 Camaro. Sports Hard tires, 100kg Ballast, restricted to just over 300hp(I think 304). Couldn't even keep up with the one-stopping RX-7 in the first stint, driving as hard as I could while stretching the tires to get over 20 laps with the first set and trying to lose as little time as possible. Stop, take no fuel, and start reeling him in. Take the lead on lap 33 a little over an hour into the race, a couple laps before he pits. Give up the lead on my 2nd pit stop and then run him down. After a battle(yes, I actually managed to have a fight with an AI car somehow) that lasted for 2 or 3 laps I took the lead on lap 55, as my tires were nearing the point that he would be faster than me. Managed to hold him off by 2.8 seconds for the win after 2 hours 20 minutes of racing as hard but smooth as I could and with NO spins, crashes, or other mistakes costing more than a couple of tenths at a time.
Oh, and for some reason I found it really amusing that the driver of the RX-7 was named F. Eisenhauer.