Slice sweet potatoes into round slices, about 1/4 inch thick.: The kitchen will fill with a fresh starchy scent as you slice the sweet potatoes , and uniform thickness ensures even cooking. When slices are about a quarter inch, they soften through consistently without falling apart. If slices vary widely, some will overcook while others remain firm, so take a little extra time to match sizes. A common mistake is cutting too thin, which can lead to mushy pieces during the long simmer.
Melt butter over medium heat in a large skillet and add sweet potato slices to the skillet.: As the butter melts you will notice a rich, creamy aroma and the surface will shimmer. Once the sweet potatoes hit the pan they will begin to sizzle faintly, picking up a gentle toasty edge. This initial contact helps coat each slice so the later glaze adheres well. Avoid high heat here, which can burn the butter and create off flavors; if you smell anything sharp, lower the burner right away.
Pour sugar and water over sweet potatoes. Stir gently, reduce heat to low, and then cover with a lid and cook until the sweet potatoes are fork tender, about 1 hour.: When the sugar meets the warm butter and sweet potatoes you will hear a soft bubbling as the mixture begins to dissolve, and a glossy sheen will form over the slices. The water helps break down the sugar into a syrup without clumping. Stir gently so you do not mash the slices, focusing on even coating. A pitfall here is stirring too vigorously, which can break the sweet potatoes and make the dish grainy if the sugar does not fully dissolve.
Remove from heat and stir in vanilla extract. Spoon the glaze over the sweet potatoes. The glaze will thicken as it cools.: As the pan simmers on low, steam will rise under the lid and soften the sweet potatoes , and the surface will slowly turn tender and translucent. You will hear only a quiet simmer, and the aroma becomes deeply spiced and caramelous. This long, low cook allows the flavors to meld and the glaze to thicken around the slices. Resist the urge to hurry by increasing the heat, as too much temperature will evaporate the glaze and risk burning. One mistake to avoid is lifting the lid too often, which releases steam and lengthens the cook time.
Remove from heat and stir in vanilla extract.: Taking the skillet off the burner releases a soft cloud of warm spice, and adding vanilla extract now preserves its fragrant top notes; stir gently and you will see the glaze take on a slightly deeper color and fragrance. Spoon the glossy sauce over the sweet potatoes so each slice is lovingly coated. If you add the vanilla while the pan is scorching hot, its aroma can fade, so removing from heat first helps retain that delicate scent. A common slip is adding extract too early, which can mute its impact.
Spoon the glaze over the sweet potatoes. The glaze will thicken as it cools.: As the dish cools in the skillet you will watch the bubbling slow and the syrup cling more tightly to each slice, creating that irresistible sheen. Use a spoon to baste so the flavors stay concentrated on top, and allow a few minutes of resting time to let the sauce set. If served immediately piping hot, the glaze may be looser, so a brief hold improves texture. Avoid storing while piping hot, as trapped steam can make the glaze watery.