Summer Vegetable Tower

Name: Summer Vegetable Tower
Ingredients: 1 pound small potatoes; Kosher salt; Pepper; 1 tablespoon plus 2 teaspoons extra-virgin olive oil, plus more for brushing; 1/4 teaspoon smoked paprika; 8 ounces multicolored carrots, sliced 1/2 inch thick on the bias; Beet Muhammara, for serving (see Note); Green Tahini, for serving (see Note); Grilled ciabatta bread, sliced vegetables—such as radishes with greens, pattypan squash, thinly sliced fennel, sliced Persian cucumbers, endive spears, Romanesco and/or cauliflower florets, blanched Broccolini, and blanched green and/or wax beans—for serving; Edible flowers and herb sprigs (optional), for garnish