FOR THE CROUTONS:
1 pound slightly stale sourdough or country bread, thickly sliced
1/3 cup extra-virgin olive oil
FOR THE SALAD:
4 to 5 cups cucumber chunks, preferably thin-skinned, such as Kirby or Persian
Kosher salt and freshly ground black pepper
2 to 3 pounds cherry tomatoes, halved, or ripe tomatoes, cored and cut into chunks
8 to 12 ounces halloumi or bread cheese
2 garlic cloves
1/2 cup extra-virgin olive oil, plus more as needed
2 tablespoons thinly sliced red onion or scallions, plus more to taste
2 to 3 tablespoons coarsely chopped fresh mint or basil
2 tablespoons red wine vinegar, plus more as needed
Make the croutons: Heat oven to 400 degrees. Cut each slice of bread into 1-inch-wide strips. Tear each strip into 1-inch pieces, removing the crust as you go if it is very thick. Transfer to a large baking sheet (or use 2 sheets, if necessary to prevent crowding). Drizzle with olive oil and toss until evenly coated.
Bake until golden brown and crunchy on the outside, 18 to 22 minutes, rotating the baking sheet and turning the croutons halfway through so they brown evenly, and checking them every few minutes. Taste and adjust the seasoning with a light sprinkling of salt, if needed. Let cool on the baking sheet.
Make the salad: In a colander in the sink, toss the cucumbers with about 1/2 teaspoon salt. Place a bag of ice cubes or an ice pack on top to chill and firm the cucumbers. Let drain while you prepare the other ingredients.
In a large bowl, combine the tomatoes with about 1/2 teaspoon salt. Toss and set aside while you prepare the other ingredients.
Slice the halloumi about 1/4-inch thick, then cut into bite-size strips. Smash and peel the garlic cloves and combine with 1/2 cup extra-virgin olive oil in a small bowl to steep.
Pour off excess liquid from the bowl holding the tomatoes. Add drained cucumbers, red onion or scallions, fresh herbs and 2 tablespoons vinegar to tomatoes and toss well. Remove and discard the garlic cloves from the extra-virgin olive oil, add the oil to tomatoes and mix well. (If desired, the salad can be made up until this point and refrigerated for 30 minutes to 1 hour. Drain off excess liquid in the bottom of the bowl before proceeding.)
When ready to serve, add about half the croutons to the salad and toss so they can absorb the liquid. Taste and adjust the seasonings with salt, pepper, extra-virgin olive oil and vinegar.
Cook the halloumi: Line a plate with paper towels and lightly coat a nonstick skillet with extra-virgin olive oil. Heat oil over medium-high until rippling. Working in batches, cook the halloumi strips on both sides until golden-brown and crusty, about 1 minute per side. Remove to the plate to drain.
Taste and add more croutons to salad as desired. (If there are too many, the salad will be starchy; too few, and it will be wet.) At the last minute, toss in the halloumi, add another good glug of extra-virgin olive oil, mix gently and serve immediately. (If desired, transfer to a clean bowl or platter for serving.)