This is how I do it:

**1. Figure out and memorize an EO cross**
This will take more moves than a regular cross, but will make figuring out the rest of the solution a lot easier.

**2. Track the 4 F2L slots**
EO will help here since the amount of cases you'll run into will be reduced, no cube rotations will be necessary for the insertions, and you'll only need to track edges' positions without having to worry about their orientation.

**3. Track the orientation of 3 of the corners for OLL**
This is the hardest/most annoying part for me. What I do is always track the same 3 corners: UBL, UBR, and UFR (A, B, and C in Speffz). Once you figure out how those 3 will be oriented after F2L, you'll know the OLL case (the 4th corner's orientation can be deduced by the orientation of the first 3). I solve OLL by rotating the corners in place, so I won't have to worry about OLL affecting PLL. There's no need to do anything about the edges since you know they'll be oriented.

**4. Track the position of 2 corners for PLL phase 1**
In step 3, you track the orientation of 3 corners (A, B, and C), so for PLL you can track the position of just two of them (A, and B) and figure out where C and D end up after F2L (C will be the 3rd piece you tracked in step 3, D will be the remaining corner). In case you're not familiar with Speffz, let's label the corners of a solved top face like this:

A - B

D - C

Now, let's say after step 3 you know A, B, and C will end up in the positions marked with an X, the remaining corner will be D:

X - D

X - X

Then, in step 4 you figure out the positions for A and B:

B - D

X - A

Based on the information from step 3 you'll be able to deduce the position of the 4 corners:

B - D

C - A

**5. Track the position of 3 edges for PLL phase 2**
I always track UB, UR, and UF for this (A, B, and C in Speffz). It's a lot easier than the corners because once again, you don't have to worry about their orientation.

**6. Figure out PLL and solve**
Using Speffz, a solved top face will be any of the following:

A - A - B

D - X - B

D - C - C (Fully solved)

D - D - A

C - X - A

C - B - B (U' away from solved)

C - C - D

B - X - D

B - A - A (U2 away from solved)

B - B - C

A - X - C

A - D - D (U away from solved)

So let's say you get this after tracking the corners and edges:

B - B - D

A - X - C

C - D - A

Then you'll have to solve this very simple puzzle in your head to figure out which PLL it corresponds to. You can notice that the edges are solved relative to each other, so you'll only need to permute the corners to finish the solve. That B - B on top is a block that's already solved, meaning you only need to permute D, C and A (an A perm), to reach this position:

B - B - C

A - X - C

A - D - D

And then perform a single U turn to finish the solve.

Example solve:

Plz ignore the smug attitude at the end. It was a video response to a kid claiming he could memorize a cube and solve it blindfolded by tracing all the pieces as he solved it in his "mental cube". He posted a video of him staring at a cube for 45 min then solving it for 2 min as proof, and I told him I could replicate his video by just doing a standard SpeedBLD solve.

**Scramble:**
F2 U' B2 L2 D' L2 U R2 F2 L2 F' L D2 B L' U2 R F2 U R

**Solution:**
F' L U2 B D2 L2 D' L2 // EO Cross

U2 R U' R' // 1st pair

U' L R' U2 R L' // 2nd pair

L U L' U2 L U' L' // 3rd pair

U2 L' U2 L U2 L' U L // 4th pair

R U R' U R U2 R' L' U' L U' L' U2 L // OLL

y' l' U R' D2 R U' R' D2 R2 x' // PLL

U // AUF

alg.cubing.net