Yep, pretty much, though the particle itself is the energy, not some kind of energy it gives off.
Mass and energy are convertible between each other, so you can think of it as the black hole losing mass equal to the mass of the particle, if it helps.
So is the energy that pinnochio gives off the hawking radiation?
Correct or more accurately it is the Hawking radiation.
I love it when the math checks out years later chefs kiss
Yep, pretty much, though the particle itself is the energy, not some kind of energy it gives off.
Mass and energy are convertible between each other, so you can think of it as the black hole losing mass equal to the mass of the particle, if it helps.