Heat the olive oil, shallots, and red pepper flakes in a small pot over medium-low heat. Cook, stirring occasionally until the shallots and red pepper flakes start to sizzle and the oil a bright orange. Remove from the heat and let cool enough to taste without burning your mouth. Season with salt and pepper.

Combine the yogurt and lemon juice in a bowl. Season with salt and pepper. Spoon into a bowl and swirl in the sizzled shallot mixture.