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Place a non-stick pan on a low heat, add the olive oil. Once the oil is hot, add the sliced onion and cook for 15-20 minutes until golden and softened. Then add the chopped garlic and carrots along with the sugar and balsamic vinegar to start the caramelisation process. Leave to cook for 8-10 minutes.
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While the onions are cooking, add the potato and sweet potato/ squash to a large saucepan, add water and bring to the boil and cook for 20 minutes. It should be partially cooked but still slightly firm at this point.
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Once both the onions and potatoes are ready, preheat the oven to 190c. Drizzle a baking tray with olive oil and place it in the oven to heat the oil while the oven gets up to temperature. While the oven is heating up, add everything from both pans to a food processor with the dried thyme and chilli flakes. Process on low until everything is combined and smooth enough to hold together, but still have some texture.
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Divide the mix into four roughly equal servings and shape them into a burger patty and place them on a baking tray. For the best results, leave them in the fridge to chill and firm for roughly 20 minutes, but they can be placed straight in the oven.
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Toss the chopped sweet potatoes in a large mixing bowl with the chilli powder and maple syrup. Remove the heated oil tray from the oven then spread the fries evenly across the tray.
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Place both baking trays in the oven and cook for 25-30 minutes until the fries are golden and starting to crisp.