The two shades of brown aren’t that important so just one style of brown is fine.
So I started with spraying the whole thing brown and then tried doing the white regions with acrylic. It got really tricky doing the letters and the mountain. Even with the smallest brush I could find, it came out pretty bad:
Paint it brown, let it dry, cover the whole thing in painters tape (get a wide roll to avoid going batty applying it). CNC through the tape, then make sure the tape is pressed down around the edges of the cut. Paint the recesses, peel off the tape, and touch up.
I have done it this way in the past with some decent luck.
Paint all recessed areas first, dont need to be precise with over painting.
Run the piece through a wide belt sander, or use a orbital sander to sand any paint from the top.
Take a foam roller and roll the brown paint over the top, using little to now pressure and light coats. This will ensure no paint runs down into the lettering.
