A lot of that stuff in the "cake is going to be hop matter, dead yeast, and other junk. to reduce this you can put it in sanitized container with a little bit of the pale ale and swish it around. Let it sit and decant the beer looking stuff into the fermenter. The yeast that is still suspended in the beer is the strongest of the bunch and should get going pretty fast.
I just used this approach for the first time 2 weeks ago. I went from a Pale Ale to an Oatmeal Stout and so far everything has gone great.
Brewing Next: Stout
Fermenting: APA with Pils and Saaz, German Pilsner, DunkelWeizen