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Heat 1 Tbsp oil in a small skillet over medium heat until it shimmers. Add hazelnuts and cook, stirring occasionally, until golden, 2 to 3 minutes. Cool slightly in skillet.
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Cook bacon in a large skillet over medium heat until crisp. Transfer to paper towels to drain and reserve 1 Tbsp bacon fat. Break bacon into 1-inch pieces.
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Purée hazelnuts (with any remaining cooking oil), vinegar, lemon juice, 1/4 tsp salt, remaining vegetable oil, and reserved bacon fat in a blender just until nuts are finely chopped (dressing will be thick and slightly chunky).
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Toss frisée, radishes, and bacon with dressing.