Toast coriander, fennel, and cumin seeds in a saucepan over medium heat until fragrant (about 1 minute).

Transfer toasted seeds to a plate to cool.

Grind the cooled spices finely.

Return ground spices to the saucepan.

Add olive oil, onion, shallot, bell pepper, garlic, carrot, and sherry vinegar to the saucepan.

Bring the mixture to a gentle simmer over low heat.

Cook until bell pepper is crisp-tender (about 8 minutes).

Add thyme and saffron, and season with salt.

Let the escabeche mixture cool completely.

In a large bowl, combine crab and parsley.

Pour the cooled escabeche mixture over the crab and parsley.

Gently toss to combine, being careful not to break up the crab.

Refrigerate for at least 4 hours, or preferably overnight, to chill.

Serve chilled with crusty bread.