Cook noodles in boiling water according to package directions; drain. Rinse under cold water; drain and place in a large bowl.
Combine cilantro and next 3 ingredients (through shallots) in a food processor; process until very finely chopped.
Heat a Dutch oven or large saucepan over medium-high heat; add the oil to pan, and swirl to coat. Add cilantro puree to pan; sauté 5 minutes. Stir in broth, sugar, soy sauce, salt, and coconut milk.
Add green onions to pan; cook 3 minutes, stirring occasionally. Stir in peas, and cook 3 minutes. Remove pan from heat; stir in cooked noodles. Set aside.
Heat a large non-stick skillet over medium-high heat. Add olive oil to pan, and heat until the oil begins to shimmer. Meanwhile, sprinkle tilapia fillets with salt and pepper. Place fillets in the pan, being careful not to crowd the pan or the fish will steam rather than sear (this step may be done in two batches depending on the size of your pan). Cook 4 minutes on each side or until fish flakes easily when tested with a fork and is golden brown on each side. Remove from pan; keep warm. Repeat procedure with any remaining fillets.
Spoon coconut noodles into large serving bowls and place a fillet on top of each serving. Garnish with chopped cilantro if desired. Enjoy immediately.
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