How to Make It
Heat oil in a large saucepan over medium until shimmering, about 3 minutes. Add peppers, onion, and garlic, and cook, stirring occasionally, until softened, about 6 minutes.
Meanwhile, using your hands, crush tomatoes to equal about 1 cup, reserving juices in a separate bowl. Add crushed tomatoes, white wine, oregano, and anchovy fillets to pan, and reduce heat to low. Cook, stirring occasionally, until flavors have melded, 1 hour to 1 hour and 30 minutes, adding reserved tomato juice as needed to keep sauce loose and chunky.
Season to taste with salt and sugar. (Keep in mind the sauce is served cold so it will need a little extra seasoning.) Spread in an even layer on a rimmed baking sheet, and refrigerate sauce, stirring occasionally, until chilled, about 1 hour.
Combine 11/2 cups cacciatore, lemon juice, and salt in a blender, and process until smooth, about 20 seconds. With blender running on medium speed, drizzle in oil until emulsified, about 30 seconds.
Preheat oven to 300°F. Pulse torn challah in a food processor until it forms coarse breadcrumbs, about 3 times. Spread breadcrumbs in an even layer on a parchment paper–lined baking sheet.
Process butter, anchovies, anchovy powder, and salt in a mini food processor until completely blended, about 10 seconds. Pour over breadcrumbs, and toss to coat. Spread in an even layer. Bake in preheated oven until golden brown, 10 to 20 minutes.
Toss together tuna, 1/2 cup cacciatore, 6 tablespoons cacciatore vinaigrette, salt, and a drizzle of olive oil in a large bowl until tuna is completely coated. Divide mixture into 6 equal portions.
Place a 31/2-inch metal ring mold on a plate. Fill ring with 1 portion tuna mixture; smooth top. Remove ring. Carefully place 1 egg yolk in center. Repeat plating with remaining tuna mixture and 5 egg yolks. Sprinkle 2 teaspoons anchovy crumbs over each tartare. Sprinkle basil leaves evenly around tartares; sprinkle each with black pepper, and top each with a spritz of lemon juice.