Preheat the oven to 350 degrees and line 2 large sheet pans with parchment paper.
Combine the flour, salt, and baking soda in a small bowl.
Cream the peanut butter and butter in a mixing bowl with a hand mixer.
Add the eggs and beat until combined well.
Add the sugars, heavy cream, and vanilla mixing again until combined.
Slowly add the flour mixture with the mixer on a low speed until it is fully integrated.
Mix in any desired chips, otherwise spoon or scoop onto sheet pans. Use a fork to gently press cross hatches into the tops & sprinkle with sugar, make thumbprints and fill with jam or just pop them in the oven as they are.
These cookies will spread nicely, so there's no need to flatten them very much. In fact, it is better to leave them in more of a ball or tall dome to ensure a thick and chewy middle.
Bake for 12-13 minutes, remove when still a little shiny or wet looking. Allow to cool on the baking sheet for 15 minutes to prevent them from falling apart.