How to increase butter fat prior to browning?
The way to get more butter flavor is to use more butter.

The water's going to evaporate, and the solids are what brown.

So even if it's a high-moisture butter, you just need to cook it down 'til the water stops foaming (water evaporating), then brown it to the level you like.

Adding cream or something else in there is just going to make a mess.