Cherry-Smoked Coffee-Rubbed Tomahawk Steak with Garlic-Horseradish Sauce

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Two 32- to 36-ounce tomahawk steaks

Olive oil, for drizzling 

Coffee Rub, recipe follows

Garlic-Horseradish Sauce, recipe follows

Lemon-Thyme Grilled Marinated Seasonal Vegetables, recipe follows, for serving

Coffee Rub:

1/4 cup ground instant coffee

1 tablespoon smoked paprika 

1 tablespoon dark brown sugar

1 teaspoon cayenne pepper 

1 teaspoon ground cumin 

1 teaspoon dried mustard 

1 teaspoon dried thyme 

Kosher salt and freshly ground black pepper 

Garlic-Horseradish Sauce:

1 1/2 cups mayonnaise

1/4 cup red wine vinegar 

1 tablespoon Creole mustard 

2 teaspoons prepared horseradish 

1 teaspoon sugar 

2 cloves garlic, minced 

Kosher salt and freshly ground black pepper 

Lemon-Thyme Grilled Marinated Seasonal Vegetables:

1 cup extra-virgin olive oil, plus more for the grill grates

1/2 cup fresh lemon juice (from about 4 lemons) 

3 tablespoons finely chopped fresh thyme 

2 tablespoons finely chopped fresh rosemary  

1/2 teaspoon sugar 

Kosher salt and freshly ground black pepper 

1 bunch asparagus (approximately 12 pieces), bottoms snapped off 

1 red onion, cut into 1/2-inch slices 

1 red bell pepper, cut into 1-inch slices  

1 yellow squash, sliced lengthwise 1/4 inch thick  

1 zucchini, sliced lengthwise 1/4 inch thick