In a saucepan on medium-high heat, stir together the curry paste with 2 tablespoons of the coconut milk (preferrably the creamy part from the top). Fry for two minutes, stirring occasionally.
Add the remaining coconut milk and all other ingredients to the saucepan. Stir to combine until smooth.
On low-medium heat, simmer the sauce for about 10 - 15 minutes, stirring occasionally. The sauce will thicken up a little bit while cooking, but will get even thicker to dipping consistency as it cools down a bit.
Notes
Check your Red Thai Curry Paste is vegan, as some brands contain fish or shrimp. For a quick replacement for curry paste, use three parts minced garlic, one part grated ginger, and either two parts fresh red chilies, one part red chili flakes or ½ part red chili powder. For more substitution ideas and serving suggestions, see the post above.