One of the best basses I own is a 1955 Fender Precision. It has a one-piece ash body, a maple neck, and a single-coil pickup that's like the one in a Telecaster guitar. It also has a string-through-body bridge; the neck is big but very comfortable. Because of the pickup position, the bass doesn't read open harmonics, but it has this beautiful, big, open, dry sound that's woody-and yes, it's so woody that it might give you a pudgy. It's a trip! Oh, I almost forgot: It also has a contoured body shape, not the big-ass plank body.
Vega, Bobby (2015) Precision Obsession: My '55, '58 & '60 Fender Precision Basses. In: Bass Player, Vol. 26, No. 2, pp. 82. Available at https://openmusiclibrary.org/article/1029365/.