Preheat your oven to 425ºF. Line a rimmed baking sheet with parchment paper for easy cleanup.
Toss the radishes in 1 tablespoon olive oil. Spread in an even layer on the baking sheet and season with 1 teaspoon kosher salt. Roast for 20 minutes.
While the radishes are roasting, marinate the chicken. In a medium size mixing bowl, combine the 1/4 cup olive oil, 2 tablespoons dijon mustard, finely chopped shallot + garlic, thyme and 2 teaspoons kosher salt. Add the chicken thighs and toss to coat. Allow them to marinate on the counter while the radishes are roasting.
After the radishes have been cooking for 20 minutes, remove the sheet pan. Push the radishes to the bottom half of the sheet pan. Spread the chicken thighs in an even layer on the top half of the sheet pan. Return to the oven and roast another 20 minutes.
Make the yogurt feta sauce. In a food processor, combine the feta, yogurt and lemon juice. Whip until smooth. If needed, add in a tablespoon or 2 of water to thin to desired consistency.
After the chicken and radishes have been roasting for 20 minutes, remove the sheet pan from the oven. Turn your oven to BROIL. There will most likely be juices on the pan released from the chicken. I tilt the sheet pan over the sink to pour a majority of the juices off so the chicken can get caramelized in the final bake.
Push the chicken to the top 1/3rd of the sheet pan, and the radishes to the bottom third. In the center, add the asparagus. Drizzle the asparagus with 1 tablespoon olive oil and season with 1 teaspoon kosher salt.
Return to the oven and BROIL for about 5-7 minutes, until the chicken is caramelized and getting golden brown, and the asparagus is soft.
Serve warm with the yogurt feta dip.
Leftovers will keep in an airtight container refrigerated for at least 5 days, or frozen for at least 6 months.
As always, lots of tips, FAQs and substitution info in the Recipe Notes below!