Ubisoft's Chessmaster: Grandmaster edition does that
Using the Mentor > Game Analysis... functionality gives the spoken annotation requirement.
For the example below I went to the Academy section and chose a game from the Database. Then this was sent to the Training mode. Lastly, I used the Mentor menu at the top to analyse the game.
The annotations are narrated by Denny Delk in Chessmaster:
Q: Whose voices are used in Chessmaster?
A: The voice used for Chessmaster (annotation, analysis, and moves) belongs to Denny Delk. The voice for illegal move commentary is Jeanne Reynolds. Their voices have been featured in Chessmaster for several years... since Chessmaster 6000.
Source: Ubi.com
Would I recommend the functionality?
No, I would not recommend this functionality of the software, because the annotations are not very insightful in my opinion. I've taken sample commentary in the game below:
[FEN ""]
[Event "Hoogovens II"]
[Site "Lone Pine, CA USA"]
[Date "1975.01"]
[Round "10"]
[White "Böhm, H"]
[Black "Timman, Ton"]
[Result "1/2-1/2"]
[ECO "c) U"]
[WhiteELO "2300"]
[BlackELO "2385"]
[WhiteCountry "NED"]
[BlackCountry "NED"]
1. c3 {A00 Saragossa Opening. A rather passive treatment by White, planning a solid strategy of controlling d4.} f5 {A00 Saragossa Opening. There is some game reference in literature to this position, but it is most unconvincing. The players of the Black pieces were universally the better players, and as the positions evolved, the better player won. Objectively you'd have to say that Black was a bit better even here.}
2. d4 {Out of Opening Book. f4 would have been in the Saragossa Opening opening line.} Nf6
3. Bg5 g6
4. Bxf6 {Pins Black's pawn at e7 with a partial pin and attacks Black's rook at h8.} exf6 {Removes the threat on Black's rook at h8. Black wins a bishop for a knight. Material is even.}
5. e3 d5
6. h4 h5
7. Nh3 Bd6 {Enables the short castle.}
8. g3 c6
9. Nf4 {Attacks Black's pawn at g6 and blocks Black's pawn at f5.} Kf7 {Removes the threat on Black's pawn at g6.}
10. Nd2 Nd7
11. Bd3 {Clears the way for a kingside castle.} Nf8
12. c4 dxc4 {Threatens White's bishop.}
13. Bxc4+ {Checks Black's king. White wins a pawn for a pawn. Material is even.} Kg7 {Moves it out of check.}
14. Qb3 {Clears the way for a queenside castle.} Qe7
15. a4 a5
16. d5 Rb8
17. O-O b5 {Slightly better is g5.}
18. axb5 {Removes the threat on White's bishop, threatens Black's pawn at a5, and isolates Black's pawn at c6 and Black's pawn at a5.} cxb5 {Attacks White's bishop. Black wins a pawn for a pawn. Material is even.}
19. Bd3 {Slightly better is Bxb5.} a4 {Moves it out of immediate jeopardy and attacks White's queen.}
20. Qd1 {Moves it to safety.} Bxf4
21. exf4 {White wins a bishop for a knight. Material is even.} Qd6 {Threatens White's pawn at d5 and blocks White's pawn at d5.}
22. Qf3 {Removes the threat on White's pawn at d5.} Nd7 {Takes the knight away from the edge of the board.}
23. Rac1 Nc5
24. Bb1 Bd7 {Slightly better is Bb7.}
25. Ba2 Rhe8 {Takes control of the open file.}
26. Rfe1 Rxe1+ {Forks White's king and White's rook at c1. Black wins a rook. Black is ahead by a rook in material. The game ends in a draw.}
1/2-1/2
I've never found comments such as "Slightly better is g5" to help in my training.
This is partly because computers are better at pointing out variations (the answer to "what should I have played?") as opposed to natural language descriptions (the answer to "why should I play that?").
This sentiment is also shared by Boris Spassky
From computers you need variations. The evaluation you need to forget.
Source: Attributed to Boris Spassky in The Wisest Things Ever Said About Chess, authored by GM Soltis