How to design a square wave inverter circuit without an op amp
Here is what I get with the 2N3904 driven with a clean 12V square wave (note that the 555 model is not very accurate, but that doesn't matter here). Collector is open except for the 10K resistor to +12:
There is a slight delay in the rise due to charge storage effects but no such waveform.

Is there a hidden capacitor or probe model or something of that ilk not shown? It would take a huge capacitance (~10nF) to cause that effect.
Here is the simple circuit:
Version 4
SHEET 1 880 680
WIRE 400 16 288 16
WIRE 288 128 288 96
WIRE 672 128 288 128
WIRE 288 144 288 128
WIRE 400 144 400 16
WIRE 80 192 64 192
WIRE 128 192 80 192
WIRE 224 192 208 192
WIRE 64 208 64 192
FLAG 288 240 0
FLAG 400 224 0
FLAG 64 288 0
FLAG 288 128 Vcollector
FLAG 80 192 Vin
FLAG 672 192 0
SYMBOL res 224 176 R90
WINDOW 0 0 56 VBottom 2
WINDOW 3 32 56 VTop 2
SYMATTR InstName R1
SYMATTR Value 10k
SYMBOL res 272 0 R0
SYMATTR InstName R2
SYMATTR Value 1K
SYMBOL voltage 400 128 R0
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR InstName V1
SYMATTR Value 12
SYMBOL voltage 64 192 R0
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR InstName V2
SYMATTR Value PULSE(0 12 10n 10n 10n 50u 100u)
SYMBOL npn 224 144 R0
SYMATTR InstName Q1
SYMATTR Value 2N3904
SYMBOL cap 656 128 R0
SYMATTR InstName C1
SYMATTR Value 10n
TEXT 30 312 Left 2 !.tran 300u