Newly rebuilt Holley 4000 on a 312 YBlock in a TBird. All works well except there is a terrible gap/sputter when coming off idle. At a stop sign when I apply pressure to the gas pedal slowly as normal, there is a terrible hesitation. If I apply gas more quickly it goes right through it without trouble. It even happens when getting back on the gas after slowing a little for a turn etc..

Any thoughts?

Thanks very much

Check timing.  Y blocks like about 10 degree initial.

Look down carb to see if you get squirts when moving the carb linkage


54 Victoria 312;  48 Ford Conv 302, 56 Bird 312
Forever Ford
Midland Park, NJ

Have you checked that the vacuum pot(s) on the distributor is functioning?  You didn’t mention if this was a ’55 or a ’56 and the distributor vacuum pot is different between these two year models.  The ’55 had a single pot design while the ’56 had a two pot design.  The vacuum advance working properly can be checked with a timing light on a running engine while varying the rpms.
 
Assuming the distributor is advancing correctly, then the accelerator pump is at the top of my list.  I have had a lot of trouble with the leather accelerator pump seals so I try to use the rubber seals whenever possible.  The Daytona brand carb kits for the Teapots come with the rubber accelerator pump seals and are also ethanol compatible.  Another possibility is the inlet fuel channel steel ball at the bottom of the accelerator pump fuel well that’s not sealing properly against its seat.
 
I’ll suggest looking in the carbs’ primary air entry holes (choke plate holes) and working the throttle at different speeds while watching for the accelerator fuel pump streams from the accelerator pump nozzles.  This will help to determine if this is something related to how fast the throttle is moving in relation to when the fuel actually squirts from the nozzles located above the venturies.

Lorena, Texas (South of Waco)

Open the idle feed adjustment screws another 1/2 turn & try it