After some research i can't find any author that has bothered to provide a line against 6.Bd3 in the saemisch or early developments of the light squared bishop in this type of position.

Intuition tells me that they cannot be very critical but after a quick research in the database i saw GM Granda Zuñiga play 6.Bd3 and win against another GM.

After some work i found 6.Bd3 Nc6!? to give some concrete problems for white. At the end of the post you will find some analysis but i am still in the dark ??? about what to do if white postpones Bd3 and plays 6.Be3 (g5) and after c5 (that is what i play most of the time) he goes d5 followed by Bd3. Any ideas? 

6.Bd3 Nc6!? Variations

1.d4 Nf6 2.c4 g6 3.Nc3 Bg7 4.e4 d6 5.f3 0–0 6.Bd3 Nc6!? (Black attacks the center whithout delay and plans to invade the d4 square) 7.Be3 

7.d5 (Looks good but with) Ne5! (Black will get to exchange the bishop) 8.Nge2 Nfd7 9.b3 Nxd3+ 10.Nxd3 c6 11.Bg5 h6 12.Be3 cxd5 13.cxd5 b5!? (Another idea would be 13. .. a6!?) 14.Qxb5 Rb8 15.Qd3 Qa5 16.Kf2 Ba6 17.Qd2 Bxe2 18.Nxe2 Qxd2 19.Bxd2 Bxa1 20.Rxa1 0–1 Umstead,G-Fishbein,A/New York 1997/EXT 2001 (37)]

7...e5 8.d5

[8.Nge2? Ng4! 9.fxg4 exd4 10.Nxd4 Nxd4 11.0–0 Qh4 0–1 Delobel,A-Whiteley,A/Cappelle la Grande 1994/EXT 2004 (30)]

8...Nd4 9.Nge2 Nh5 10.Qd2 c5 11.dxc6 bxc6! 12.0–0 f5 13.exf5 gxf5 14.Bg5 Bf6 15.Bxf6 Qxf6 16.Nxd4 exd4 17.Ne2 c5 18.Ng3 Nxg3 19.hxg3 Bd7 20.Kf2 Rae8 21.Rh1 Re3 0–1 Petri,T-Kersten,U/Hermannen 1997/EXT 2001 (36).