Chop the baby yellow potatoes into small half-inch cubes and slice the cremini mushrooms.
Heat the olive oil in a large skillet over medium-high heat.
Add the potatoes to the skillet and cook, stirring occasionally, until they are golden brown and tender, about 8-10 minutes.
Season the chicken breast with sea salt, black pepper, and dried thyme.
Move the potatoes to one side of the pan and add the chicken breast, searing for 5-6 minutes per side until the internal temperature reaches 165°F.
Remove the chicken and potatoes from the skillet and set them aside on a plate.
In the same skillet, add the sliced mushrooms and minced garlic, sautéing until the mushrooms have released their moisture and browned.
Pour in the chicken broth to deglaze the pan, using a wooden spoon to scrape up the flavorful browned bits from the bottom.
Reduce the heat to low and stir in the Greek yogurt and fresh spinach until the sauce is creamy and the spinach has wilted.
Return the chicken and potatoes to the skillet, tossing everything together to coat in the garlic sauce before serving.