If not already done, drain and rinse the canned white beans. Pat dry lightly with paper towel or let sit in a colander for a minute.
Toast the 4 slices of whole-grain bread to your desired crispness and set them aside.
In a small bowl, combine 1/2 cup drained white beans, 2 teaspoons tahini paste, 1 teaspoon lemon juice, and 1/4 teaspoon kosher salt. Mash with a fork until mostly broken down, leaving a little texture.
In a second bowl, combine 1/2 avocado (pit and peel removed), 1 teaspoon lemon juice, and 1/4 teaspoon kosher salt. Lightly mash with a fork until creamy but still slightly chunky.
If the grape tomatoes are not already halved, cut the 1/2 cup grape tomatoes in half.
Spread the mashed bean mixture evenly over the 4 toasted bread slices.
Spoon or spread the mashed avocado evenly on top of the bean layer on each toast.
Top the toasts with the halved grape tomatoes, distributing them evenly, and serve immediately.