Boring, positional closed defense against e4

Does anyone know a good positional, boring defense against e4?

I am looking for something like this, except against e4:

1. d4 Nf6 2. c4 c5 3. d5 e5 4. e4 d6

The modern Philidor fits the bill of a sound positional and closed defense against e4 (and I'll look for another one later...) :
1.e4 d6 2.d4 Nf6 3.Nc3 e5 4.Nf3 (because 4.dxe5 is harmless), and you're in for thirty moves of patient manoeuvering. The position is slightly worse for Black, but very boring for White if he is clueless. Black has several plans and must stay flexible. Don't bet everything on "the Black Lion" and the g5 push (which might or might not work depending on the specifics).

Avoid the move order 1.e4 e5 2.Nf3 d6 3.d4 Nf6 because White is unlikely to cooperate with 4.Nc3. Let's consider alternatives and how White can thwart Black's project:
1...e5 2.Nf3 Nc6 fails with 3.d4 and Black can't keep the position stable ;
1...e5 2.Nf3 Nf6 looks adequate, but 3.d4 can become wild ;
1...e6 2.d4 d5 3.Nc3 Nf6 is my second choice, not so positional and boring as the Modern Philidor but close (3.exd5 and 3.e5 certainly are) ;
1...c6 2.d4 d5, oh wait 3.exd5 cxd5 4.c4, ok let's forget it ;
1...c5 2.Nf3 and 3.d4, no, just kidding ;
1...d5 2.exd5 idem ;
1...Nf6 is held together by tactics (as are unorthodox first moves by Black, which might not be held together at all) ;
1...d6 and 1...g6, the Pirc/Robatsch/Modern galaxy, becomes quickly tactical if Black doesn't transpose to the Philidor.

In general, keeping the position stable after 1.e4 requires White's cooperation. Likewise, it requires Black's cooperation and willingness to be slightly worse for a long time. If we dig deeper, I'm sure White can stir up trouble in the classical French and Modern Philidor as well, but it might be far-fetched. Maybe the Petroff is a good option too after all, but specialist knowledge is needed to compare how "quiet" these lines really are after a dozen moves.

Sounds like you want the French classical version. Its a snooze-fest.

Try playing c6 as the third move in the French Defense, e. g.

1. e4 e6 2. d4 d5 3. Nc3 c6
2. e4 e6 2. d4 d5 3. e5 c6
3. e4 e6 2. d4 d5 3. Nd2 c6

This is very solid (it has the solid pawn center of the Semi-Slav) and you can convert the game from here into a closed defense with heavy maneuvering if you so choose. Another advantage is that nobody really plays this, so your opponent will be typically out of book after move 3. Hence, if you prepare your responses and play it often, it can even turn into an advantage. The computer likes it and gives just a marginal advantage to white after move 3 (which white has in all decent openings).

you cant make the game boring if ur opponent is looking for fireworks, try the caro kann maybe.

if u mean boring = solid then play e5! You dont want to spend years learning an underdog systems. Instead play rich positions, where you can choose whether to play " boring".
I can highly recommend Bologan's book Black weapons in the open games as a repertoire book for that.

Caro-Kann is nice boring positional play with simple black-plan. I playing only Caro for e4 and the same system for d4 (Slav defense, as a rule.

If you seek solidity, the Caro-Kann (1.c6) and 1.e5 are both excellent choices from which you can steer the game into quiet waters most of the time, but achieving this consistently requires tremendous knowledge of opening theory. Even so, there is a reason that 1.e4 openings are called "open" games and 1.d4 are called "closed" games; it's quite hard to get a completely closed position (like the one you mentioned) after 1.e4 without some serious cooperation from the opponent.

1...e5 is pretty good for that. You can play 25 moves in the Ruy Lopez without a single capture.

Try D5