I know a single star is almost surely more massive than a single brown dwarf, but consider a case: a very small star is orbiting a very massive brown dwarf which has a very massive moon, such that the total mass of that brown dwarf and its moon is larger than that of the star. Not counting capturing, is this type of system possible (formed naturally)?
If a brown dwarf count as a star in this case, the solution is as easy as a smaller brown dwarf orbiting a larger one.
If not, it is still possible if you have two brown dwarfs orbiting close to each other, both just too small to be red dwarfs, together out-massing an orbiting red dwarf, just large enough to be counted as a star.
While I have no example of such a system, the Alpha Centauri system has to closely orbiting stars, with a more distant star orbiting, and Luhman 16 is a system with two brown dwarfs orbiting each other.
The differences between a brown dwarf and a low mass star are based upon their mass. A brown dwarf does not have central temperatures and pressures to create energy using hydrogen fusion. The mass is too low to create these conditions. A star by definition is an object where energy is created using hydrogen fusion. This happens when the core temperature/pressure are high enough. This requires a higher mass. The exact mass boundaries between planet, brown dwarf and star are not fully determined. They also depend somewhat on composition. Even so there is no real chance of having a brown dwarf more massive than the lowest mass star. The masses could be similar.
In terms of orbits: any pair of bodies orbit around their common center of mass (barycenter). They orbit about each other. When the two objects are the same mass the barycenter is half way between them. When say one star is ten times the mass the barycenter is nearer (1/10th the distance) the more massive star. Think of a see-saw with unequal weight people on it. Now the less massive object (say planet) orbits about a much more massive object (star) the barycenter is inside the star. So we can say the planet orbits around the star. In realality they are both orbiting around the barycenter.