I agree with most in here 
My normal line is to continuation bet 90+% of the HU pots and why change it now?
lets look at the possibilities after a continuation bet (which of course would be more or less a full pot bet on this very connected board):
a) Villain got trash (folds) - True, we did not get much value from our monster, but would villain give us much action if this board didn't hit him even if we checked to him? My guess would be that he would slow down after we calls (or raises which would only make him fold) his flop bet and check behind on the turn.
b) The flop hits the villain partly (calls) - With his TP a regular fish will call us down anyday if we normally cont bet alot (we should be able to get AI on the river and hopefully stack him off) ♦
c) The flop hits the villain good (raises) - With his top two pair, set or straight + flush draw he will most likely raise us (both for value [he would think] and to give us bad odds to draw out on him [useless if he knew our hand, but whatever]). This can get interesting, the flop goes:
Hero bet 0,38$ - MP3 raise to 1,10$ (5,63$ remaining - 4,59$ effective) - Hero?
call, raise (push that is) or fold
(just to make undercover happy)? - Personally i would raise it anyday to put maximum presure on the villain - he could be on a draw (remember we can still lose if he hits a FH with his set/two pair or we can risk a split if he raised us in the first place with TPTK or something like that).
The pros on a call on the other hand are that he could have raised us for info to get away from a medicore hand relatively cheap and would fold to an AI. Anyway as i said - AI would be correct in this case - the pot has already grown relatively big and we would like to take it down now and we can't allow him to draw out on us cheaply.
d) The flop hits gives the villain a straight too (raises) - He could sit there with AQ too, and the money would most likyly come to the middle on the flop - that is if we chose to reraise the villain AI in the scenario i made in c) - In this rare case it is of course best to get all the money in as early as possible, since we are ahead (split on the flop, but we got the prescious flush draw too). If we don't get the money in and another ♥ or a card that pairs the board falls on the turn, it could possibly kill the action and money would be lost.
To sum up: Bet this flop as you would bet it with any other hand - Everytime! Your hand is very strong, but not unbreakable - Do not slowplay it!
I think that enough for now 
Comments are very welcome, I'm here to learn as wee (I'm very new to NL, and have just returned to playing poker after exams, summer holiday and then moving into a new appartment - but you will be seing alot more of me from now on again)
Best regards,
Mugge
Btw, where is Stefan?