Clean fish, following steps 1 and 2 of "You Found the Fish," below.
Combine garlic, mint, salt, and pepper with 1/3 cup oil in a large bowl. Spoon half into a medium bowl. Add sardines to large bowl and pat them all over outside and in cavities with mint mixture. Set aside.
Heat grill to high (450° to 550°). Add tomatoes to medium bowl with 1 tbsp. vinegar. Turn gently to coat. Brush bread with remaining 1 1/2 tbsp. oil.
Oil cooking grate, using tongs and a wad of oiled paper towels. Grill fish, covered, until marks appear and fish release when nudged with tongs, 2 to 3 minutes; gently roll over and cook other side, about 2 minutes. Transfer fish with a wide spatula to a board. Grill bread, turning once, until edges are browned, 1 to 3 minutes.
Fillet fish (see step 4 below). Top each toast with arugula, then a tomato slice (leave juices behind), then a sardine fillet. Stir remaining 1 tbsp. vinegar into tomato juices, spoon a little over bruschetta (save the rest for other uses), and serve immediately.
You Found the Fish--Now What? Some markets will clean them for you, but if not, you can do it yourself easily enough--it just takes a little practice.
SCALE AND CUT. Scrape off the scales gently with fingertips. Cut through both sides of belly 1/4 in. from edge, from collar to tail.
CLEAN. Pull out the guts; rinse the fish inside and out. Snip off fins.
FILLET (RAW). Score fish all the way around collar just to the bone. Slide your index finger into cut on one side of collar and your middle finger into the other side. Slide your fingers along spine to tail, pulling fillets free. Cut off tail and pull out any remaining bones.
FILLET (COOKED). Make 3 cuts through flesh to bones: along the length of the spine (to one side of it), at collar, and just above tail. Slide knife under fillet to free it from spine, and lift it off. Pull up tail and lift off spine and head to free bottom fillet. Pull out any remaining bones.
Note: Find these little fish at some grocery stores, fish markets (you might need to order them), and Asian markets. If you live near a coastal town, head to the docks-fresh anchovies and smelt are often sold as bait. Look for fish with bright eyes, shiny skin, and a mild aroma. They're very perishable, so plan to cook them the same day.
Note: Nutritional analysis is per appetizer serving.