In a medium skillet, heat oil over medium-high heat. Once the oil is hot, add the diced shallot and minced garlic, stirring to combine. When the mixture begins bubbling (after 1–2 minutes), reduce the heat to medium-low.
Cook the shallots and garlic over medium-low heat for 20–25 minutes, stirring occasionally, until they turn golden brown and crispy. Take care not to let them burn.
In a small bowl, combine dried minced onion, red pepper flakes, kosher salt, chili powder, and paprika.
Set a fine-mesh strainer over the bowl with the seasoning mixture. Pour the hot oil mixture through the strainer, allowing the oil to drain into the seasonings. Leave the crispy shallots and garlic in the strainer and set them aside to cool.
Once the shallots and garlic have cooled completely (about 20–30 minutes), add them back into the seasoned oil and stir to combine.
Transfer the chili oil to a clean jar with a tight-fitting lid. Store at room temperature in a cool, dark place for up to several weeks. Stir well before each use.