Heat 1 tablespoon oil in small saucepan over medium heat. Add quinoa and allspice; stir 2 minutes until toasted. Stir in 1 1/2 cups water and pinch of salt. Cover; reduce heat to low. Cook 15 to 20 minutes until quinoa is tender. Transfer quinoa to large mixing bowl to cool completely.
Add bell pepper, fennel, cucumber and tomatoes to bowl. Add remaining olive oil, fresh lemon juice, 1 teaspoon salt and pepper to taste. Stir to combine. Add parsley and mint. Stir again to combine. Season to taste, if desired.
Serve immediately, or store in airtight container in fridge up to 1 day.