I just ran a new Imperial through Bleak Falls Barrow with a two hander on Adept difficulty (the middlest difficulty). I got there at level two and found no challenge at all - however I've played the dungeon over twenty times and know exactly what to expect.
My "build" was, one point into twohanders and one levelup on health. My visible armor rating was 70, and I had a (Fine) Iron Greatsword.
Instead of just answering "what's a good two-hander build for level 2?", I'll provide many tips for "I'm having trouble with combat in bleak falls barrow as a two hander user, what can I do better?"
There is a wolf on the road to bleak falls barrow. If that wolf bites you, you are highly likely to contract rockjoint, which causes you to do 25% less damage with melee weapons. Check your "Active Effects" under the Magic menu. If you are diseased, go to WhiteRun to cure the disease at a shrine for free, or buy a potion of cure disease from the shop in Riverwood (~250 gold).
You have a healing spell, but the tutorial doesn't do a good job of telling you about it. You should be using this spell outside of combat to heal to full. You can put the spell on both hands and heal to full in combat, before resuming attack. I didn't need to heal during combat in my run.
Swinging a twohander is slow. Your movement is also slow while you're swinging. This means you can't adjust your range once your swing starts. While twohanders have more range than one handers, you might not be experienced enough to use that range. Instead - close hard with the enemy before swinging - you shouldn't tolerate missing. When enemies die in 3-4 swings, you don't want to take 5-6 swings due to missing.
Power attacking requires stamina and more time. Just use normal attacks and not power attacks. Then you can ignore stamina. Well, that's effective but not very fun. A more advanced technique is to weave normal attacks with power attacks. Start a normal attack. During the normal attack animation, start a power attack. In about the same amount of time as a power attack, you'll do a normal attack AND a power attack.
Wear all four armor pieces (head, hands, feet, chest). You get 100 hidden armor points for filling all four slots with items that require armor skill.
Upgrade all of your armor and your weapon. Even if your blacksmith skill isn't leveled - do the upgrades. If you don't know how to upgrade gear, take the tutorial in the first town, or at the smith's in Whiterun. The gear you use should always be upgraded.
Save the game every few fights. There are some number of "boss" encounters which may require as many as 8 swings of a two hander. It is a sad thing to have to restart the dungeon because a "boss" surprised you and your game isn't saved.