It does look like a cross between a 335 and a studio LP. Meet:
Patty the Blueshawk
"Say hello to Patty the Blueshawk, a Gibson model that was made from 1996 to 2006. If you've seen Wonderland with John Mayall, you've seen Patty. It has a Fender-like 25 1/2"-scale neck, a through-body bridge, distinctive Blues 90 pickups, and a 6-way Varitone. Plus, it weighs only 7 pounds—packing plenty of sonic muscle for its class. Wonderland swapped a Tele for Patty and she loves the way its P-90s cut through in the Bluesbreakers."