Line a pan for chilling. Lightly oil an 8x8-inch baking dish or line it with parchment, leaving overhang for easy lifting.
Heat the liquid. In a medium saucepan, bring 4 cups water or broth to a simmer.
Season with 1 teaspoon kosher salt.
Whisk in polenta. Slowly sprinkle in 1 cup polenta while whisking to prevent lumps. Reduce heat to low and cook, stirring often, until thick and creamy, 20–25 minutes. Add splashes of water if it gets too thick before soft.
Enrich and season. Stir in butter or olive oil, grated Parmesan, minced garlic, and a few grinds of black pepper.
Taste and adjust salt.
Chill to set. Spread polenta into the prepared dish, smoothing the top to about 1/2 to 3/4 inch thick. Let cool, then refrigerate until firm, at least 1 hour (or overnight).
Make the tomato relish. In a bowl, combine diced tomatoes, minced red onion, chopped basil and parsley, red wine vinegar or lemon juice, a drizzle of olive oil, a pinch of red pepper flakes, and salt and pepper to taste. Let it sit 15–20 minutes to meld.
Cut the polenta. Lift the chilled slab onto a cutting board and slice into bite-size squares or rounds.
Pat surfaces dry with a paper towel for better browning.
Pan-sear until crisp. Heat a large nonstick or cast-iron skillet over medium to medium-high heat with a thin layer of olive oil. Sear polenta pieces 3–4 minutes per side, undisturbed, until deep golden and crisp. Work in batches; don’t crowd the pan.
Season and serve. Transfer to a tray and sprinkle with flaky salt.
Spoon tomato relish on top or serve on the side so the bites stay crisp. Garnish with extra herbs and a final drizzle of olive oil if you like.