Preheat oven to 350°F (177°C). Line an 8-inch square pan with parchment paper.

Using a handheld or stand mixer fitted with a paddle attachment, beat the butter and brown sugar together on medium-high speed until combined, about 3 minutes. (Here’s a helpful tutorial if you need guidance on how to cream butter and sugar.) Scrape down the sides and up the bottom of the bowl with a silicone spatula and then add the vanilla extract. Beat on medium-high speed until combined, about 30 seconds. Add the flour, baking powder, salt, and oats. Beat on medium speed until combined. Scrape down the sides and up the bottom of the bowl and beat again as needed to combine. Mixture will appear dry and be crumbly. You will have between 3–3.5 cups of crust/crumble mixture.

Lightly press a little more than half of crumble mixture into bottom of prepared baking pan. (You want a little more mixture for the crust than for the topping.) Bake for 12 minutes.

Whisk sweetened condensed milk, lemon juice, and lemon zest together. Mixture will be thick.

Pour and spread filling over pre-baked crust (while crust is hot). Sprinkle the remaining crumble mixture on top.

Return bars to the oven and bake for 22–25 minutes or until edges are very lightly browned and appear set. Avoid over-baking. Remove from the oven and place the pan on a wire rack. Cool bars completely.

Lift the bars out using the parchment paper overhang on the sides. Cut into squares.

Cover leftover bars and store at room temperature for up to 2 days or in the refrigerator for up to 1 week.