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Step 1
Adjust rack to top position and preheat oven to 450 degrees. Wash and dry all produce.
Step 2
Peel and grate or mince garlic. Halve tomatoes; toss on a baking sheet with half the garlic, a large drizzle of olive oil, and pinch of salt and pepper. Roast on top rack until tomatoes are lightly charred, 8-10 minutes. Transfer to a medium bowl. Carefully wipe off sheet with paper towels.
Step 3
Meanwhile, pick parsley leaves from stems; mince leaves. Mince chives. In a second medium bowl, combine ricotta, half the Parmesan (save the rest for serving), and half the minced herbs. Season with salt and a pinch of chili flakes to taste.
Step 4
In a small bowl, combine remaining garlic and a large drizzle of olive oil; season with salt and pepper. Brush one side of each slice of sourdough with garlic oil. Place on baking sheet used for tomatoes. Bake on top rack until toasted, 4-5 minutes total.
Step 5
Remove sheet from oven; add walnuts to same sheet. (TIP: If sourdough is done at this point, remove from sheet.) Return to oven until walnuts are toasted, 2-3 minutes. Once cool enough to handle, roughly chop walnuts.
Step 6
Divide toasts between plates; spread with herby ricotta. Evenly top with tomatoes, walnuts, and remaining Parmesan. Sprinkle with remaining herbs and chili flakes to taste. Drizzle with as much balsamic glaze as you like and serve.