The simple answer is not to use a brush, and don't use water-based varnish. Use an old-school solvent-based PU; get an empty bottle, pour in one part of varnish and one part white spirit (mineral spirits in the US), ie a 50% cut in the varnish. Shake the bottle well and wipe the mix on thinly and evenly with a lint-free cloth - an old cotton pillowcase or sheet will do fine. Work facing the light so that you can see any spots you've missed or puddled it. Leave it to dry properly - at least overnight - then repeat until you have the finish you want. You want a warm dry room with no dust and no flies around. You can cut it back slightly between coats with fine abrasive paper or 0000 steel wool. Remove the sanding dust with a tack cloth..

Dispose of the mix-soaked rags safely, since they can spontaneously combust, given the right conditions.

It's a fairly good rule when you're applying most finishes - use a number of thin coats, rather than one thick one. This method is pretty foolproof, and it doesn't take long to apply a coat. You need patience between coats though, and it takes around 5-6 coats if you need a hard-wearing surface like a table top. If you don't like the glass-like finish (it doesn't suit country-style furniture), then cut back your final coat with 0000 steel wool and apply a coat of good wax polish.

HTH.