Wash, core and seed the green peppers and cut into long thin strips. In a deep casserole, put both vinegars, the sugar, salt and halved garlic cloves. Bring to a strong boil, then add the green peppers and cook for 10 minutes. Remove the peppers from the liquid and place on paper towels to dry.
Put a layer of green peppers into a glass jar and cover with some chopped garlic, a pinch of capers, a few small anchovy pieces and a few basil leaves. Add a second layer of green peppers and repeat the process until all the ingredients have been used. Top with basil. Add fresh oil, a little at a time, pressing the jar contents down with your fingers to force the oil well down into the jar and thoroughly coat all the ingredients. At least 1/2-inch of oil must cover the top and any air pockets must be eliminated. Seal the jar hermetically and store in a cool dark place for 20 days.