I have to ask why this particular approach, which looks
doomed to marginal (at best) efficiency. The only thing
I see to like, is self-oscillation. But oscillation can be
easily had, and pulse width control that takes the
inductor just shy of saturation is about the best you
can do for current-throw - but this "joule thief" looks
to have no particular control for that (other than the
selection of base resistor, sloppy at best).
I'd bet a Diodes Inc minimal boost chip costs the same
or less than a power transistor. In fact I'll bet you a million
Venezuelan bolivars. Make that two. I see one on digi-key,
looks like a SOT-23 w/ 0.5A output, adjustable voltage,
for $0.50 while a 2N3055 costs $6.40. Even your lowly
2N2222 costs $2.58.
Unless you like wasting time and money building an
inferior outcome (who can say?) you probably ought to
check out the modern world.
https://www.digikey.com/product-det...ated/AP3012KTR-G1/AP3012KTR-G1DICT-ND/4505297