Turn the heat under a stovetop pressure cooker to medium-high and add the avocado oil. When the oil starts to shimmer, add the dried red chile. Cook, stirring, until deepened in color and puffed up, a few seconds. Add the cumin and fennel seeds and the turmeric and cook until deepened in color and flavor, about 30 seconds.
Add the beets and stir to coat. Add the brown sugar, tamarind paste, salt, if using, and 3/4 cup water. Stir well. Secure the pressure cooker lid and bring to high pressure over medium-high heat. Once at a high pressure, cook for 13 minutes. Turn off the heat and carefully release the pressure using the quick-release valve, then remove the lid. Pour the contents into a blender along with 1/4 cup olive oil and process until smooth. Taste and adjust the seasoning until you like it.
Meanwhile, add the remaining 2 tablespoons olive oil to a nonstick skillet over medium-low to medium heat. Pat the halloumi well with paper towels until it's dry. Place the halloumi in the skillet and cook on each side until golden brown, about 2 minutes per side. Remove to a paper towel-lined plate.
Spoon the beet chutney into a small side dish. Add the fries to a platter, then sprinkle with mint and pomegranate seeds. Serve immediately.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.