Combine almonds and oil in a small saucepan over medium heat; cook, swirling often, until almonds are just golden, about 4 minutes. Using a slotted spoon, transfer almonds to a blender; let almonds and oil cool. Pulse almonds until finely chopped. With motor running, slowly add cooking oil, vinegar, sugar, and 1/4 cup water and process, adding water as needed, until just thinner than peanut butter; season with salt.
Bring vinegar, sugar, coriander, salt, and red pepper flakes to a boil in a small saucepan; reduce heat and simmer, stirring, until sugar is dissolved, about 3 minutes. Add carrots and let cool.
Heat oil in a large skillet over medium-high heat. Add carrots; cook, turning often, until golden and tender, 5-8 minutes. Add garlic and butter; cook, tossing, until garlic is golden, about 2 minutes. Season with salt and pepper.
Spoon almond purée onto plates and top with pickled carrots, sautéed carrots, cilantro, mint, and sesame seeds.
