Make the Togarashi Pita Chips: Preheat the oven to 350°F. Split each pita in half horizontally into 2 rounds, then stack and cut those four rounds into 8 triangles (you should get 32 pieces total). Whisk the olive oil, togarashi, and salt in a large bowl, then add the pita chips and toss to coat.
Arrange the pita chips on 2 rimmed baking sheets and bake, stirring once midway through, until the chips are crisped and golden, 11 to 13 minutes. Season with more salt to taste.
Make the Edamame Hummus: Bring a large pot of salted water to a boil. Add the edamame and cook according to package directions; drain, reserving ¼ cup of the cooking water.
Reserve 2 tablespoons of the edamame, then add the rest to a food processor along with the reserved cooking water, tahini paste, olive oil, lemon juice, garlic, and salt. Process until smooth, about 30 seconds.
Season with more salt to taste and sprinkle with togarashi and reserved cooked edamame. Serve with togarashi pita chips.