Warm Salmon Filets with Fennel Emulsion and Provençal Olive Oil

Name: Warm Salmon Filets with Fennel Emulsion and Provençal Olive Oil
Ingredients: 1 tomato, peeled, halved, and seeded; 2 Tbsp. extra-virgin olive oil, preferably Provençal; 6 loosely packed cups fennel fronds (feathery green parts); 1 1 ⁄ 4 cups fish fumet (concentrated fish stock); 3 Tbsp. heavy cream; 1 tsp. pastis (optional); 4 6-oz. skinless center-cut salmon filets; 8 Tbsp. butter, softened; 2 Tbsp. lemon juice; 1 tsp. Asian chili oil; Salt and freshly ground black pepper; 1 Tbsp. peeled, minced red bell pepper; 3 Tbsp. minced dill; Coarse sea salt