The key is having all of your items prepped before you start melting the sugar. First steps are dicing butter and getting it to room temperature. Second step is heating the heavy cream either in the mircrowave or on the stove top. You want it warm when it goes into the melted sugar. Also have your salt and vanilla measured and ready to go.
Add sugar to a large heavy-bottom pan. Turn heat just under medium if using gas and medium if using electric. It's not going to change for several minutes. Once you start seeing a gold color develop, begin stirring by gently working the sugar from the outside into the middle. A rubber spatula is good for this job. You want to avoid stirring in a way that causes splashing so a hard rim doesn't form on the sides of the pot. Once you begin stirring, you'll do it until the sugar is fully melted.
Clumps will form as the sugar heats. That's okay. Keep stirring until everything has melted. By now it will be an amber color.
As soon as the sugar is fully dissolved remove the pot from the burner entirely. It will be an amber color. You need to move quickly. Add the butter and whisk it in until almost fully incorporated followed by the warm cream. Slowly pour it in while whisking. Add the salt and vanilla and whisk until inforporated and then pour in a jar to cool and thicken.