First, make sure you're free of distractions. Caramel needs some alone time with you.
In a large pot (make sure it's larger than you think you'll need), bring together the sugar, water and corn syrup over medium-high heat. Stir until the sugar is moistened, then continue stirring constantly until sugar melts, about 5-7 minutes. Sugar may melt into a liquid, then clump up - this is normal and you should continue stirring, trying to break up the clumps with your rubber spatula or wooden spoon. Eventually the sugar will liquefy again and within seconds begin turning a caramel color. Cook, stirring constantly, until a dark amber color is achieved. BE CAREFUL because this color comes and goes pretty quickly, and you want to make sure you pull it before it burns.
Once the deep amber color is reached (or desired color is reached), immediately add in the butter and stand back briefly as the mixture will bubble considerably. Continue stirring until butter has melted and mixture becomes creamier. Remove from heat and stir in the heavy cream, being wary of the mixture bubbling aggressively. Stir until the cream is incorporated, then sprinkle in the salt and stir to combine.
Allow the mixture to sit for about 15 minutes before pouring into mason jars with lids or another heat-proof container with a lid. Mixture will be very hot. Allow to cool to room temperature for the mixture to adequately thicken and settle. Store in the fridge for up to a month.