How to Make It
Preheat the oven to 450°. In a small bowl, cover the apricots with boiling water and let stand until softened, about 15 minutes. Drain the apricots; discard the water.
In a food processor, puree the apricots with the butter until smooth. Scrape into a small bowl, add the thyme and season with salt and pepper. Transfer 1/4 cup of the apricot butter to another small bowl and whisk in 3 tablespoons of the oil to make a glaze.
Place the chicken on a rack set over a rimmed baking sheet. Season the cavity with salt and pepper. Squeeze the lemon halves all over the chicken, then stuff them in the cavity and tie the legs together with twine. Rub the remaining 2 tablespoons of oil all over the chicken and season with salt and pepper. Carefully pour the broth onto the baking sheet.
Roast the chicken for 35 minutes, until golden. Brush with half of the apricot glaze and roast for 10 minutes. Brush with the remaining glaze and roast for 5 to 10 minutes longer, until an instant-read thermometer inserted in the thigh registers 165°. Tilt the chicken to release the juices from the cavity, then transfer the chicken to a surface and let rest for 15 minutes.
Strain the juices into a bowl; skim off the fat. Season with salt and pepper. Carve the chicken and serve with the pan jus and remaining apricot butter.