Remove the seeds of 4 pickled plums (umeboshi). Finely chop the skin and flesh, then use the flat side of the knife to flatten and mash it into a paste.
Add the umeboshi paste, 1 tbsp Japanese light soy sauce (usukuchi shoyu), 2 tbsp mirin, 1 tbsp rice vinegar and ¼ tsp dashi granules to a small saucepan and heat on medium while stirring occasionally.
When the mixture starts to boil, reduce the heat to low and let it gently bubble for about 30 seconds while stirring continuously to prevent burning.
Pour the mixture into a heatproof jug and add 1 tbsp olive oil and 1 tbsp toasted sesame oil. Whisk until combined.