How to Make It
Stir together tomatoes, bell pepper, carrot, fennel, oil, and garlic in a large saucepan. Heat over medium-high until mixture starts to sizzle, about 2 minutes. Reduce heat to medium, and cook, stirring occasionally, until tomatoes break down and stick to bottom of pan, 20 to 25 minutes. Add shrimp shells; increase heat to medium-high, and cook, stirring often, until shells are orange in spots, about 2 minutes.
Add peppercorns, bay leaf, parsley, and 7 cups water. (Water should just cover shrimp shells.) Bring to a boil over high. Reduce heat to low, and simmer until broth has a shrimpy aroma, about 1 hour. Skim off any foam. Remove from heat, and cool 10 minutes. Pour through a fine wire-mesh strainer into a bowl; discard solids. Use immediately, or store in an airtight container in refrigerator up to 2 days or in freezer up to 3 months.