To prepare tomatoes: Prepare an ice-water bath and bring a large pot of water to a boil. Make a shallow “X” cut on the bottom of the tomatoes. Place tomatoes in boiling water and blanch for 1 minute. Using a slotted spoon, move the tomatoes to ice water bath. Once cooled, gently peel off skins. Cut out the stems with a paring knife. Cut tomatoes into halves and carefully squeeze out the juice and seeds, then finely chop.
Place prepared tomatoes into a medium mixing bowl. Add oil, vinegar, salt, pepper and basil; toss together and set aside. Adjust the top oven rack to six inches below heating element and pre-heat the broiler. Place bread slices in a single layer on a baking sheet; lightly brush each side with olive oil using a pastry brush. Broil slices in oven for about 2 minutes per side or until golden brown. Remove from oven and immediately rub toasts with clove(s) of garlic.
In another bowl, mash avocado well with lemon juice; season with salt and pepper to taste. Spread mashed avocado mixture onto each slice of toast, then generously spoon tomato topping on top.