Secondly I used another coil, this is a single coil on a single bobbin, it measures:
no ferrite: 3.8mH
bottom ferrite only: 11mH
Both ferrite halfs: 110mH
the series resistance of this coil's circuit is 10Ω (including R1 and RDS(ON)
of Q1), then the time constants (L/R) of these LR circuits will be, respectively:
380μs for the 3.8mH inductance
1.1ms for the 11mH inductance
11ms for the 110mH inductance
These are the times needed for the current to reach 63% of the V/R limit - which is 3A if a 10Ω circuit is supplied with 30V.
You are however pulsing it with only 10μs, so during that time, the current through the coil will only reach:
2.6% of 3A (or 78mA) for the 3.8mH inductance
0.9% of 3A (or 27mA) for the 11mH inductance
0.09% of 3A (or 3mA) for the 110mH inductance
Thus, it is not surprising that you are not seeing a clear current ramp at this pulse width and time scale.
To see it well, the pulse width has to match the time constant L/R ...at least approximately.