Doughnuts with Grapefruit-Vanilla Jelly

Combine sugar, grapefruit juice, and pectin in a large saucepan; scrape in seeds from vanilla bean.

Cook over medium heat, stirring, until sugar dissolves.

Increase heat to high; whisk until mixture boils vigorously, about 6 minutes.

Pour mixture into a shallow glass baking dish. Let cool completely at room temperature. Cover, and chill until set, at least 2 hours.

DO AHEAD: Can be made 1 week ahead. Keep chilled.

Lightly coat a large bowl with olive oil. Heat juice in a small saucepan over medium heat until an instant-read thermometer registers 110°–115°. Remove from heat; whisk in yeast. Let stand until mixture becomes foamy, about 10 minutes.

In a stand mixer fitted with a dough hook, mix 3 1/2 cups flour, 2 Tbsp. sugar, eggs, grapefruit zest, salt, 2 Tbsp. olive oil, and apple-juice mixture on medium speed until a sticky dough forms, 4–5 minutes. Transfer to oiled bowl. Turn to coat; cover with a kitchen towel. Let dough rise in a warm, draft-free place until doubled in size, about 1 hour.

Gently roll out dough on a floured surface to ½” thickness. Cut out rounds with 1 ½” biscuit cutter. Place on lightly floured baking sheets. Let rise until doubled, 30–40 minutes.

Place a wire rack inside a rimmed baking sheet; set aside. Pour remaining 1 cup sugar into a wide shallow bowl; set aside. Attach a deep-fry thermometer to side of a heavy pot. Pour vegetable oil into pot to a depth of 2" and heat over medium heat to 350°. Working in batches, carefully add doughnuts to oil. Fry until golden brown, about 2 minutes per side, allowing oil to return to 350° between batches. Using a slotted spoon, transfer doughnuts to rack; let drain for 2 minutes. Roll in sugar in bowl to coat.

Transfer grapefruit jelly to a pastry bag fitted with a 1/4" metal tip or squeeze bottle. Pipe a little more than 1 tsp. jelly into each doughnut. Serve immediately.