Start the polenta. Combine the milk and water in a medium saucepan and bring to a gentle boil. Whisk in the polenta in a slow, steady stream, then reduce heat to low. Cook, whisking every few minutes, for 30 minutes, until thick and very creamy. Season generously with salt and pepper as it cooks — don’t wait until the end.

Time to make the pangrattato. While the polenta cooks, heat the olive oil in a small skillet over medium heat. Add the breadcrumbs and a pinch of salt and toast, stirring constantly, for 3 to 4 minutes, until deeply golden. Off heat, stir in the lemon zest and parsley. Set aside uncovered — covering traps steam and softens the crunch. Note: make this in the same pan you’ll use to sear the chicken and build the sauce — fewer dishes.

Pat the chicken breasts completely dry, skin and all. Season both sides generously with salt and pepper.

Heat the olive oil in a large stainless or cast iron skillet over medium-high heat until shimmering — not smoking. Lay the chicken skin-side down and do not touch it for 8 minutes. After about 4 minutes, press down gently with the back of a spatula or a pot lid to keep the skin in full contact with the pan. At 8 minutes, the skin should be deeply golden and crisp.

Flip the chicken and immediately add the butter to the pan. As it melts and foams, baste the flesh side continuously, tilting the pan to pool the butter and spooning it back over the chicken again and again. Cook for about 6 minutes, basting the whole time, until the chicken reaches 160 degrees Fahrenheit (71°C) internally.

Transfer the chicken to a rack, skin-side up, while you build the sauce. If you don’t have a rack, a large plate works — just keep the chicken in a single layer.

Now it’s time to work on the sauce. Pour off all but about 2 tablespoons of fat from the pan. Add the sliced garlic and lemon zest and cook over medium-low heat for 30 to 45 seconds, just until fragrant — pull it before the garlic colors, or it turns bitter.

Pour in the white wine and scrape up every browned bit from the bottom of the pan. Let it bubble and reduce by about half, 60 to 90 seconds, before adding anything else. This is what separates a sauce that tastes built from one that just tastes like wine was added.

Next, add the cherry tomatoes, cover, and cook for 3 to 4 minutes to steam them until they’re about to burst. Uncover and continue cooking for another 3 to 4 minutes, letting some of the tomatoes collapse fully into the wine while others stay just intact.

Remove the pan from the heat. Add the cold butter a couple of cubes at a time, swirling the pan to melt each addition into the sauce before adding more. This is what gives you a glossy, emulsified sauce instead of a greasy one. Stir in the lemon juice, then fold in the torn basil.

Now, finish the polenta. Off heat, stir the butter and Parmesan into the polenta until melted and smooth. Taste and adjust salt and pepper — it should taste fully seasoned on its own, not rely on the sauce to carry it.

Spoon polenta onto plates or a platter and set the chicken on top, skin-side up so it stays crisp. Spoon the tomatoes and sauce around the chicken. Finish with the pangrattato and flaky salt, if you’d like.