Prepare the vegetables: Peel the cucumber, halve it lengthwise, remove the seeds, and dice. Break the cauliflower into small florets and wash. Peel and wash the carrots, then cut into matchsticks. Clean and thinly slice the mushrooms, lightly dressing with lemon juice. Trim and clean the radishes. Wash the cherry tomatoes.
Prepare the mustard sauce: In a salad bowl, whisk together the mustard, ketchup, minced garlic, a splash of lemon juice, olive oil, salt, and pepper until smooth.
Prepare the aioli: In a bowl, whisk 2 room-temperature egg yolks with 1 tablespoon mustard. Let rest for 1 minute, then slowly drizzle in the olive oil while whisking vigorously to emulsify. Stir in ketchup, salt, and ground pepper to taste.
Presentation: Arrange the prepared vegetables in verrines or small serving glasses. Serve the mustard sauce and aioli in jam jars alongside for dipping.
