Begin by chopping the carrots and potatoes into large chunks, creating colorful, rustic pieces that will soften beautifully during slow cooking.
Season the chicken breasts generously with salt, pepper, and a pinch of paprika to enhance their flavor.
If you like, quickly sear the chicken in a hot skillet with a splash of olive oil until golden brown on both sides—this step adds extra depth of flavor and color.
Layer the chopped carrots and potatoes at the bottom of the slow cooker, spreading them out evenly to ensure they cook uniformly.
Place the seasoned chicken breasts on top of the vegetables, ensuring they are slightly spaced to allow heat circulation.
Add the whole garlic cloves and sprigs of fresh thyme around the chicken for fragrant infusions that will permeate the dish as it cooks.
Pour the chicken broth over everything, ensuring the ingredients are partially submerged to promote even cooking and flavor absorption.
Cover the slow cooker and set it to low heat, allowing everything to cook gently for 6 to 8 hours until the chicken is tender and falls apart easily.
After cooking, gently shred the chicken with two forks if you prefer smaller pieces, or serve whole for a rustic presentation.
Taste the broth and vegetables, adjusting seasoning with salt, pepper, or a squeeze of lemon if desired to brighten the flavors.
Remove the thyme sprigs and garlic cloves, then serve the hot, tender chicken and vegetables in bowls, spooning over the flavorful broth for a comforting finish.