“Double-check” is a compound verb. Perhaps you are preparing your annual tax return (declaración fiscal) and you think it is reasonable to “double-check” it in case there is a mistake. This “double-checking” is a process of reviewing the numbers for a second time, to check if they are correct.
So ”double checking” (una doble comprobación) is the noun, the activity.
So mortals often double-check (comprobar de nuevo/volver de comprobar/asegurarse bien de que) their work.
You can also double-check things with people. Perhaps you have heard a rumour about a person, and you want to double-check the issue with that person (confirmarlo con algn) before accepting – as true – the rumour.