In a large 5-6 quart, heavy bottomed pot, measure sugar in an even layer. Heat the sugar over medium-high heat, whisking as the sugar begins to melt. The sugar will be clumpy at first, but will melt down as it continues to cook.
When the sugar has completed melted, stop whisking. Tilt the pan, or use the whisk to gently move the sugar around in the pan as the sugar cooks. When the sugar reaches 350 degrees F on a candy thermometer, or turns a light amber color, add all the butter at the same time. The sugar will bubble angrily when you do this, so be careful. Whisk the butter into the sugar until it is completely melted and then remove the pan from the heat.
Slowly add the half & half to the sugar, whisking as you pour. Again, the sugar will bubble up angrily, so be careful. Whisk until all the half & half is incorporated and smooth. Add the kosher salt and whisk to blend well.
Let the caramel cool for 15 minutes before storing in a glass jar. Allow caramel to completely cool to room temperature before storing in the refrigerator. The caramel will keep for up to two weeks.
The caramel will harden in the fridge, so allow to come to room temperature before using in recipes requiring a pour or drizzle. For recipes in which it will be mixed right in, cold caramel is fine.
Each serving is approximately 1.5-2 Tbsp, to taste.