Using a box grater, coarsely grate the zucchini. Place the shredded zucchini in the middle of a clean kitchen towel and sprinkle with the 2 teaspoons of salt. Let sit for 5 minutes, then squeeze the towel to remove excess moisture. Repeat until as much liquid as possible has been released, then transfer the zucchini to a bowl.
Add the garlic, basil, almonds, thyme, Parmigiano-Reggiano, lemon juice, lemon zest and 3 tablespoons of the olive oil to the zucchini; toss to combine. Season to taste with salt and pepper and refrigerate for an hour.
Just before serving, drizzle the remaining 1 tablespoon of olive oil over the bread and grill or broil the bread until toasted, then let cool.
Top each slice of bread with about 3 tablespoons of the zucchini pesto and serve immediately.