Planning a Fourth of July cookout? Here’s a thought: Make it a brunch on the barbie.

Why this makes sense: With a brunch, everyone gets out of your hair earlier, so you can clean up and rest for work the next day. (By that logic, brunch makes sense for most holidays.)

But back to my point, which is to inject smoky flavor and outdoor spirit into the morning meal.

You’ve got more than a week to think about it and do your research. The menu will be dictated by the sophistication of the grilling apparatus you possess. If it’s a grill or smoker capable of covered, indirect heat at precise temperatures, you can treat it as an outdoor oven and make a bread pudding or frittata. If it’s a hibachi, think breakfast quesadillas — cheese and breakfast sausage wrapped in flour tortillas, lightly grilled. Or, hey, Spam is hibachi-friendly.

Here some ideas that would work on even the least sophisticated grill:

>> Grilled fruit: Pineapple, especially, takes on a whole new personality when it’s caramelized on a grill, but almost any fruit would work. Mango and bananas are sturdy and easily skewered. Fruits that aren’t quite stellar raw — imported peaches, say — can be elevated by grilling.

>> Grilled French bread: Make sure the grill is very clean or cover with a sheet of foil. Thin slices of bread will cook evenly and quickly. If you can set up indirect heat, you can go with thicker pieces.

>> Breakfast pizza: Use premade flatbread, naan bread or bagels; top with salsa, cheese, scrambled eggs and crumbled sausage. Grill, covered, until the cheese melts. If your grill doesn’t have a cover, tent with foil or use an upside-down disposable foil pan.

>> Grilled avocados: It is theoretically possible to crack an egg into the center of an avocado and grill them as a package — I’ve seen pictures. I’ve tried this, though, and all I can say is raw eggs are very slippery. However, an avocado on its own, halved and grilled cut side down until lightly browned and softened, is a lovely thing. Top it with an egg cooked on your stove.

This recipe combines the first two suggestions. It’s easily adapted to differing tastes. If coconut flavor is not your thing, switch out the coconut milk with half-and-half. Or, boost the coconut quotient with a sprinkle of toasted coconut flakes. Is brunch too early for rum? Maple syrup is just fine, too.

GRILLED FRENCH TOAST AND FRUIT KEBABS WITH COCONUT RUM SAUCE

• 1 dozen sweetbread rolls
• 3/4 cup coconut milk
• 2 eggs
• 1 teaspoon vanilla
• 1 teaspoon cinnamon, plus more for dusting
• 16 8-inch skewers
• 2 apple bananas, peeled, cut in 1-inch slices
• 1 mango, peeled, cored, cut in chunks

>> Sauce:

• 1 cup coconut milk
• 1 tablespoon butter
• 2 tablespoons brown sugar
• 1 tablespoon dark rum, or more, to taste

Cut rolls into quarters; spread on baking sheet and let sit overnight to dry out.

Whisk together coconut milk and eggs, then stir in vanilla and cinnamon. Pour mixture into shallow dish or rimmed baking sheet. Roll bread pieces in mixture until lightly coated on all sides. Don’t let them get soggy.

Thread bread and fruit onto skewers in any order, keeping a little space between the pieces so they cook evenly.

Prepare grill to medium heat. Cut a piece of foil big enough that a row of kebabs will fit in a single layer; coat well with cooking oil spray and place on grill. Line kebabs up on foil and let cook until lightly browned, 2-3 minutes, then turn. Keep turning until all sides are toasty and fruit is lightly caramelized. Cover grill if you like for a more smoky flavor.

To make sauce: In small saucepan, combine coconut milk, butter and brown sugar over medium-high heat. Stir to dissolve sugar, then reduce heat and simmer about 10 minutes, until sauce thickens slightly. Remove from heat and stir in rum.

Serve kebabs drizzled with sauce and sprinkled with more cinnamon. Serves 4.

Approximate nutritional analysis, per serving: 650 calories, 31 g fat, 23 g saturated fat, 110 mg cholesterol, 500 mg sodium, 80 g carbohydrate, 5 g fiber, 37 g sugar, 16 g protein