Two possible ways. The first is out of ordinary matter the same as what we are made of. Just a bunch of atoms sloshing around in space and at some point, however unlikely it may be, they all slosh around in just the right way to create the physical structure of a brain.
The second way is through quantum fluctuations. Quantum mechanics, an addition to being famously incomprehensible, is famously counterintuitive. There's a phenomenon called quantum tunneling where a particle can go from point A to point B without ever being in between. Imagine a mug full of coffee sitting on a table. Quantum tunneling would be like if the coffee could somehow travel from inside the mug to outside, on the table. Over time the mug could gradually empty out, not from evaporation, but from "leaking" out through the impermeable sides of the mug.
Perhaps even more counterintuitively, even in a completely empty vacuum, particles are constantly being created and destroyed. We all know about the law of conservation of matter: matter can't just be created out of nothing. But imagine that this law was enforced by a policeman who doesn't have eyes in the back of his head. You can create particles out of nothing when he's not watching as long as you destroy them before he turns around to look at you. You can have, for example, an electron and a positron created out of nothing that fly apart and then come back together to
annihilate each other. The time scale where this can happen is something like 10^-20 or 10^-40 seconds.
This exact mechanism is how
Hawking Radiation works. Stephen Hawking worked out how these quantum fluctuations, if they happen close to the event horizon of a black hole, can result in one of the two particles getting sucked into the black hole while the other escapes. This results in the black hole slowly losing mass over time.
So the other mechanism to forming a Boltzmann Brain in completely empty space would be through quantum fluctuations creating enough particles out of empty space.