1-First Step: Preparation/mise en place
Gather all ingredients. Soften butter at room temp for 30 minutes. Measure dry items into one bowl, wet into another. Grease pan with butter and line bottom with parchment circle for easy release. This setup prevents mid-mix scrambles.

2-Second Step: Cream butter and sugar
In a medium bowl, beat ½ cup softened butter and ¾ cup sugar with electric mixer on medium 2-3 minutes. Mixture turns light, fluffy pale yellow. Scrape sides often. This incorporates air for tender crumb in your small batch cake.

3-Third Step: Add eggs and vanilla
Beat in 2 eggs one at a time, fully incorporating each. Add 1 tsp vanilla extract. Batter may look curdled, normal. Eggs provide lift and bind flavors beautifully.

4-Fourth Step: Mix in milk
Stir in ½ cup milk gently on low speed. Avoid overmixing to keep batter light. Wet mix now ready.

5-Fifth Step: Combine dry ingredients
In separate bowl, whisk 1¼ cups flour, 1½ tsp baking powder, ¼ tsp salt. Add to wet mix in two parts. Fold with spatula or low mixer until just combined, few lumps ok. Overmixing toughens cake.

6-Sixth Step: Pour and bake
Spoon batter into prepared 6-inch pan, smooth top. Tap pan on counter to release bubbles. Bake at 350°F (175°C) 25-30 minutes. Toothpick in center comes out clean or few moist crumbs. Rotate halfway for even bake. Cool in pan 10 minutes, then wire rack fully.

7-Seventh Step: Make frosting
Beat ¼ cup softened butter until creamy. Gradually add 1 cup powdered sugar, ½ tsp vanilla, 1-2 tbsp milk. Whip to spreadable peaks. Taste, adjust milk for consistency.

8-Final Step: Frost and serve
Level cooled cake top if needed. Spread frosting evenly. Slice into 4-6 pieces. Serve room temp with berries or coffee. This single serve vanilla cake impresses at small gatherings.