This shows my attempt to make a monochromatic yellow on the left and a full spectrum mixed to make white on the right.
So is the brown just a monochromatic yellow at a lower brightness like how gray is white at a lower brightness?
Yellow is a mix of red and green only. Your sample at the left contains blue as well, and that makes it brown.
Be careful with the terms used. You asked about
monochromatic color; Jonathan's and Guillermo's answers relate to
monochromatic light. Brown is a color; if a patch has the same color, then that is a monochromatic color. However, brown is not a monochromatic light.