In the Classical Variation of the Caro-Kann, what is the most positional, strategic, quiet, slow, closed, boring, dry and solid variation for Black? I am not sure what to play as Black in the Classical Variation of the Caro-Kann, after 1. e4 c6 2. d4 d5 3. Nc3 dxe4 4. Nxe4 Bf5 5. Ng3 Bg6 6. h4 h6 7. Nf3 Nd7 8. h5 Bh7 9. Bd3 Bxd3 10. Qxd3

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  1. e4 c6 2. d4 d5 3. Nc3 dxe4 4. Nxe4 Bf5 5. Ng3 Bg6 6. h4 h6 7. Nf3 Nd7 8. h5 Bh7 9. Bd3 Bxd3 10. Qxd3


What I would like is the most positional, strategic, quiet, slow, closed, boring, dry and solid variation (the variation which is the least sharp and tactical).
And I would like to castle on the same side as White.

So what exactly should I play? And what are the differences between starting first with 10...e6 or 10...Qc7 or 10...Ngf6 ?
You are the author of a series of questions of the type "What is the most boring way to play" and whereas I am fond of positional play as well, I must say that the way the question is formulated is completely wrong. I played the Caro-Kann for years and there is simply no way to avoid an heated battle in some variations, unless you are ready to make a lot of concessions and compromise your game by getting a very passive and unpromising position.
To excel at chess, you must master various types of positions. Avoiding these will stop your progress. You cannot beat regularly stronger players by using positional means only - they will master these positions as well as you do, but are also able to play dynamically. 
Look at Petrosian's games, he was able to attack fiercely.