First thing you need to ask yourself is, how much sugar can dissolve in water at room temperature?

Because, of course, the hotter the water is, the more sugar can dissolve in it.

When the sugar has dissolved add the eggs, then the butter.

When the sugar has dissolved, season to taste with pepper and salt.

Lower the heat and simmer for 5 minutes, stirring until the sugar has dissolved.

Reduce the heat and simmer until the sugar has dissolved.

Bring to a boil and stir until the sugar has dissolved.

I think sugar would dissolve about as fast in pure water.

When the sugar has dissolved, raise the heat to high, and boil 3 minutes.

Stir until the sugar has dissolved, to make a simple syrup.