Heat oven to 350 degrees. Line a 9-inch-square baking pan with parchment paper or foil, letting a few inches hang over side of pan. Brush with oil.
Spread oats and seeds on another baking pan and toast in oven just until golden and fragrant, 6 to 8 minutes, shaking pan once.
In a saucepan, combine oil, honey, brown sugar, maple syrup and salt. Stir over medium heat until smooth and hot. In a mixing bowl, toss together toasted oats and seeds, dried fruit and cardamom. Pour hot sugar mixture over and stir until well combined.
While mixture is warm, transfer to prepared pan, pressing into pan evenly with an offset spatula.
Bake until brown, 25 to 30 minutes. Transfer pan to a rack and let cool completely. Using the overhanging foil or paper, lift out of pan and place on a work surface. Cut into bars, about 1 1/2 inches by 3 inches.
Adapted from Bill Yosses, White House pastry chef