Whats the FATTEST sounding Tube amp to warm up Lean speakers?

I have a pair of Mid Monos,  and they rock with KT88...   I have used them with several speakers ...  big and bold but still have great mid and highs.  

Any older Conrad Johnson tube amplifier within your budget will give you what you're looking for. Expect syruppy mids but less crisp highs and slightly bloated lower bass - depending on the matching with your speakers, if you're willing for the trade-off.

Whatever tubed amp you choose, load it with NOS British valves(Mullard/Brimar/Ediswan/Genelex/etc).  If those don't warm/sweeten/fatten things up enough, swap it's resistors out for carbon compositions, and/or- it's coupling capacitors, for oil in paper types.

I'll go as far to say it's not the tube amp but rather your choice of tubes. Vintage little Mullards are extremely warm sounding. Vintage Tung Sol 6550's solid plates are warm like Mullards but with the EL34's glorious mids that are known for but with a lot more low end and power. I was never a fan of current production tubes. I had the Octave V70SE and later the V110 with a black box. I even had the V40SE for a short while. All were good but as you move up the line you gained more 'control' of the music.

Agreed on the NOS Mullard EL34's. They are what I have in my Shindo Montrachet and I couldn't be happier.