Prep the artichokes: Trim the artichokes by slicing the stems and the top of the artichokes. Use scissors to snip off any sharp leaf tips. Then, slice the artichokes in half and scoop out the center furry part.
In a large pot, fill it up 3/4 of the way with water and add the sprig of thyme, 1/2 lemon juice, and about 1/4 tsp of the salt. Bring to a boil. Once the water is boiling, add in the artichokes and cover to cook for about 15 minutes. Drain the artichokes on a wire rack.
Next, preheat the grill to medium-high heat. Drizzle the artichokes with olive oil and sprinkle with the remaining salt. Grill the artichokes cut-side down for about 5 minutes. Then, flip them and cook for another 2-3 minutes pressing down gently to ensure you get that grill mark.
Meanwhile, make the dipping sauce by mixing all the ingredients in a bowl and mix. Set aside until artichokes are ready to eat. Serve and enjoy!