Lemon Oil: In a small saucepan, combine oil and lemon zest. Heat over low heat until fragrant, about 10 minutes; let cool and strain through sieve.
(Make-ahead: Store in an airtight container for up to 2 weeks.)
Crostini: Arrange baguette slices on a rimmed baking sheet. Bake in a preheated 400°F (200°C) oven until crispy and light golden, 5 to 7 minutes. Rub tops with garlic clove. Brush lightly with 1 tbsp of the lemon oil. Set aside. (Make-ahead: Cover loosely and set aside for up to 4 hours.)
Meanwhile, with a fork, mash avocados with 1 tbsp of the lemon juice, the chives and salt.
(Make-ahead: Cover surface directly with plastic wrap and refrigerate for up to 4 hours.)
Spread avocado mixture onto crostini. Toss tomatoes and bocconcini with 1 tbsp (15 mL) of the lemon oil and the remaining lemon juice. Top each crostini with 2 pieces of tomato and 1 piece of bocconcini. Top with basil and sprinkle with pepper.