Blend the peas and vegetable broth in a blender until smooth. Take the lid off and, with the motor running, pour in the oil in a steady stream to emulsify the mixture. Add the lemon juice then chill in the refrigerator for 1 hour.
To make the spicy crab, whisk the canola oil, chili paste, and lemon juice together in a bowl. Fold in the crabmeat and mint and season with a pinch of salt. Fill espresso or sake cups, about 3/4 full, with the chilled pea soup. Garnish the pea shots with a generous tablespoon of the spicy crab and serve immediately.