This is what I think would be what DeBroek could come up with:
DeBroek F-3P Falcon
Description: Completely re-designed on request of the Persian airforce. Based on the concept of the never-build F-3D the plane features an enclosed cockpit with more reliable radio, a new and more powerful engine of the LMF1200 series, a fully retractable landing gear and modified tail plane. A first prototype was assembled in late 1936, allowing a maiden flight in February 1937 folliowing some ground tests that required some redesign to enhance the pilots view forward and swept volume of the new landing gear. Should the plane proof successful in flight delivery of a first series is projected for 1938.
Type: Fighter
Power: 1x 1050hp LMF1200 IX 12-cyl.-engine (inline)
Crew: 1
Vmax: 575km/h
Vcruise: 450km/h
Range: 1500km
Weapons: 2 15mm MG, 2 7,62mm MG
[Stats based on the historical P-40 with Allison V-1710-33.]