How to sharpen blue LED voltage-to-current knee at 3.0 V?
You don't mention it but the best solution is a comparator, which is easy to set the toggle level of.  

A BJT counterpart is the transistor Schmitt-trigger:  



This website has detailed examples of the required calculations for the thresholds.

A third option is a simple NPN transistor with a 1:4 resistor divider, so that above 2.8 V in the transistor conducts and switches on the LED. The higher the HFE the sharper the corner point. That has nothing to do with the transistor's Ic-Vbe curve, but because of the higher HFE you'll reach the point where the current limiting resistor takes over more quickly. Without the current limiting resistor you would still have a current that varies with the voltage, giving a transition region you don't want.  

If you want you can make a Darlington of 2 BC337-40s, that should give you an HFE of at least 62000. Don't forget to adjust the divider to 1:2 for that.