Make the soup: Blend the peas and vegetable broth in a blender until very smooth. With the motor running, slowly pour in the olive oil in a steady stream to emulsify the mixture. Add half of the lemon juice, then chill the soup in the refrigerator for 1 hour. Season with salt and the remaining lemon juice before serving.
Prepare the crab: Whisk the olive oil, sambal oelek and lemon juice together in a bowl. Fold in the crabmeat and mint and season with a pinch of salt. Fill small cups or glasses about three-quarters of the way with the chilled pea soup. Garnish each portion with 1 generous tablespoon of the spicy crab and serve immediately.