I was recently re-reading Christoph Scheerer's chapter on the Euwe Defence with 1.d4 d5 2.e4 dxe4 3.Nc3 Nf6 4.f3 exf3 5.Nxf3 e6 and seeing that in several lines he likes the idea of Bd3 followed by Qe2. I wondered if I could find something new involving Qe2 in positions where he doesn't mention the idea.
My first experiment was a failure. Following 6.Bg5 Be7 7.Bd3 Nc6,
I've seen 8.a3 and 8.Qd2 suggested, and Lev Zilbermints has favoured the second pawn sacrifice 8.0-0 Nxd4 9.Kh1, but I wondered if 8.Qe2 might work, because after 8...Nxd4 9.Nxd4 Qxd4 10.0-0-0, White has a long lead in development and the black queen is facing the white rook on d1.
Unfortunately for me, Stockfish inconveniently points out 10...Qg4!, when White has to spend another tempo moving the queen, and Black is able to get time to consolidate.
Another variation where Christoph Scheerer doesn't mention the Qe2 possibility is after 7...c5 8.dxc5 (here 8.Qe2?! cxd4 doesn't work) Qa5.
Here he only gives the main line 9.0-0 Qxc5+ 10.Kh1, which, to be fair, gives White a fair amount of compensation for the pawn. But here 9.Qe2!? looks quite good, e.g. 9...Nbd7 10.0-0-0 Nxc5 (10...0-0 11.h4 improves over the 11.Kb1 of Toussaint-Mercky, France 1999).
Now White has various options including Ne5 and Rhf1, keeping up a fair amount of pressure on the black position, and if Black plays ...Nxd3+, White can answer with Rxd3.
Generally I think these days that 7.Bd3 c5 (as recommended by Joe Gallagher and James Rizzitano some time ago) is not so challenging for White, and that the traditional main line 7...Nc6 is the most critical.
I have most often played 7.Qd2 (instead of 7.Bd3) when I have had this line with White, but I am not sure about White's compensation after 7...c5, which is why I decided to revisit the traditional 7.Bd3.