Before you begin cooking, finish your preparations. Roughly chop the chicken thighs into bite-sized pieces, with a thickness of ½ inch (4 cm). Baby potatoes should be cut in half. Slice and peel the carrots. Finely cut the onion, mince the garlic, and chop the parsley.
In a large saucepan with a heavy bottom, heat the oil and butter over medium-high heat. Add the chicken and arrange it in a single layer. After three minutes of searing without stirring, stir for a minute. Take off the chicken before it's fully done; we'll finish it off later by boiling it in stock. Move to a fresh bowl.
Add the carrots, onion, and garlic. Cook on medium for two minutes. Add oregano, pepper, and salt and stir. Add the flour next, and whisk until well combined. After adding the chicken and potatoes, pour in the broth and insert the bay leaf. After bringing to a boil, lower the heat to medium-low, and simmer until the potatoes are soft, about 20 minutes.
Add half-and-half when ready, then simmer for an additional five minutes. Add parsley and lemon juice to finish. After tasting, adjust the spices as needed. Have fun!