That's what I thought that looked like...
T50-7 has very little inductivity, 0.0043 uH/t^2. So you need 15 turns just for 1uH, and something like this might be more typical with 25uH, or 75 turns! With only 7 turns on there, you've got more like 0.25uH, which probably isn't enough to run at any frequency (certainly not well).
On the plus side, you'll easily be able to get 75 turns in that core if it's, say, 34 gauge or smaller, which is fine for the current level.
Last one I made was a rather beefy:
Somewhere around a T30-35, not sure if it's standard. Some grab bag item. Think it was around 0.015 uH/t^2. But, this is a much more powerful converter, so it uses a proportionally smaller inductance (rated for much more current), so that's good. You can think of it as a much thicker, stiffer spring; it takes more force to push energy into it, but it stores more energy too.
20 turns, primary with 2 x 26 AWG wire (better than a single solid wire due to skin effect), secondary with 37 AWG (because it doesn't take much base current, or I'll just end up connecting resistance in series anyway). That makes 6uH, which should be something like, from 1V supply, it charges to 2A peak in 12us, for an operating frequency around 40kHz. (Actually I think the current is less than that, and the frequency higher.)
Rbb is switchable 100 ohms or 1k, for brightness control (or open circuit for "off"). Cbyp is, I think, 1uF. There's also 47uF bypassing the supply. The transistor is a PBSS4540 high current, low-Vce(sat) type. As I recall, switching performance (as determined by an oscilloscope) was worse with any base resistance (besides the winding itself), so I left that off. The output is simply strapped across a 1W white LED to ground. It's pretty bright on a fresh AA cell!
Tim